Don't get me wrong Lateralus, I wouldn't want to stop anyone from opening up their gear and exploring. I'm firmly in the camp of people learning the truth of how their gear works and being able to spot the myths by actually becoming engineering competent. Knowledge is the best antidote to believing hype and legend. It saves you from "mojo mindedness" where everything is magic so any old tosh can be stated as truth and be unquestionably believable.
The point is that, as you are aware, it is dangerous in there. Lethally dangerous! People need a certain level of skill and experience before they are safe to be left in charge of an open amp chassis. If you are sure you are at that level, (which you have already answered), I'm happy to give you any advice I can on what you can do to try to fix things.
Unfortunately you will need test gear to get to grips with most of the higher level of repair. A half decent test meter is a start and will help deal with the most common types of problem with amps. An oscilloscope is not far behind to deal with chasing signals through and finding sources of noise. I would guess you have a meter to hand but not a 'scope. Ok, onward and upwards, if you are confident you will be safe and prepared to take that in your own hands let's go.
The high voltage PSU cap in the GM36 has across it a bleed resistor, actually a pair of them, so it should drain itself pretty quickly anyway. Most decent amps have this nowadays. I would still pop a meter across the line immediately after the rectifier diodes to check every time I went inside there after the amp being on. You will know how to check out the fuse of course, just make sure to remove it from the clip or at least lift it at one end and use the meter to test for continuity, don't rely on your eyes. My guess is that you will find the fuse blown and the answer is those Russian "equivalent" 6P41Ps. They are not an equivalent at all, they cannot take the same anode voltages as the design EL84s. I suspect they have broken down and caused the fuse to blow. We have to hope that there is no other damage done as a result of this. The only way is to fix the fuse, put in proper valves and try it.
When I said "resist the urge to fiddle" I actually meant in this area of valve swapping not in general. It is never, never a good solution to alter the characteristics of an amp circuit by swapping in a different valve type unless there is a match of many parameters, not just an attractive value for one of them. And people who advise you "I tried it and it sounds amazing" are themselves sitting on a ticking time bomb playing Russian roulette with their gear. The substitutes for 12AX7s I mentioned are like that. It is unlikely that you will damage your amp with them, but you could! Every aspect of the stage will change and not for the better. There is a reason why your warranties are often invalid if it comes out that you have done so. 12AX7/5751 yes, anything else no!
You cannot change the tone of any amp markedly by changing valves. It is a myth and it doesn't stand up to proper scrutiny. In any comparison of component swaps you need to be able to compare the same amp for both examples. The change has to be made quickly, in seconds, or the ear and brain self calibrate and you forget what you have heard before the change. You then hear what you want to hear in the second. And that leads us to another absolutely essential aspect, you cannot know which you are listening to. This is the foundation of "Double Blind Listening Testing" which is the only way to genuinely see whether you or anyone can hear a difference.
Let's take tone capacitors in guitars. We all know that Orange Drops or Bumble Bees or PIOs make your production line model sound like a Custom Shop don't we? Well, as the price of those exotic caps rose and rose and rose from the everyday level which I remember them at in the '70s as they were just day to day components, to what they could screw out of you in the '00s because they were "old and golden", there came a time that Gibson started to use a cheap modern ceramic cap in their tone slots. No one blinked an eye about it at first. Then some "guru" somewhere blew the lid off and told everyone how shit their guitars now sounded and the balloon went up. Gibson were dragged through the streets for saving a few cents by using a cheap totally unsuitable cap. Only the truth is somewhat different. That ceramic cap is an extremely good component. If you bother to look at the specs you will find that it differs from the other "audiophile" caps as it has a tendency to rise in inductance at higher frequencies leading to a slight high frequency resonance. That would make it harsh sounding and explain the difference. Except this doesn't happen until you are in the region of a few MEGAHERTZ. Even bats shrug that one off and I certainly don't know of anyone with radio receiver level ears. Below that there is no distinguishable difference in the components' electrical characteristics and no one even suggests there is, they just "know" the ultra expensive tone caps sound better.
I have actually demonstrated this to people convinced they could identify their favourite cap without any problem. So, take two caps of different types but of matched values to within 1% on a small toggle switch in the guitar cavity and out of sight of the guitarist. Have a dummy switch wired in next to the real one. An independent person operates the switches and acts as manager of the test tossing a coin and taking down the results in a table. He tosses the coin and marks down what was the result. If it is heads he switches the real switch over and clicks the other dummy switch over too. If it is tails he switches either the dummy twice or he can switch the real switch twice. The dummy switch acts to remove any chance that the guitarist can perceive whether the real switch has been changed or not, in all cases there will be two switch actions. The guitarist plays for as long as he needs then guesses whether it is the "tone" cap or the other crap cap he is hearing. His result is marked down against the result of that coin toss. The guitarist must be told nothing about how his guesses are working out! The person managing the test should try to not follow what is the state of the guitar and whether the guitarist guesses correctly or not. It takes a large number of these tests to get results which can be statistically significant and prove something. If you do it only 4 times you could get 5 different outcomes in terms of correct guesses. Consider a 2correct:3wrong result. Is that enough to have a high degree of faith that the guesser cannot hear any difference? No. But if it becomes 20:30 then we are onto something. Yes it needs a bit of statistics applied to prove any result but it isn't hard to do and see whether there is any likelihood that a person can hear anything at all. I've done this with very well meaning golden eared gurus a couple of times and never had anyone show any signs of hearing a difference let alone an improvement with their own preferred cap.
Do you know what? It's always the test, or the statistics, or the other gear, or the room, or the fact they have a cold which masks it.