Good news that you weren't locked out of using your amp. I think from what you have said there that your problem is unlikely to reoccur in the short term. You may have an iffy valve in there bringing the rest down with it but it seems unlikely to become constant. The LEDs are showing you that your pairs are pretty well matched and in good condition. You have pair 1 / 4 both bang on 13 blinks which is great, and 2 / 3 are on 12 / 11 blinks respectively which is also very good. A difference of 1 blink is no problem at all as the TSC adjusts to compensate for such a small difference and matches them up automatically. I don't think there is a real burning necessity to change out those valves but, as you have ordered them, it will stand you in good stead in the future. Remember what I said about boxing the old ones up and labelling them clearly. And make sure to add the date you swapped them out to the boxes too to keep a handle on when you genuinely last replaced the valve set. You'll regret it if you don't.
Glad you went for the 5751s and not something esoteric like a 12AT7 or even something unknown from the Russian military, (yes it really happens). As you may have read me groaning about in the valve thread, they are definitely and inarguably not "substitutes" or "equivalents" or "family members". They are all totally separate valve types with no common characteristics at all. A Honda gearbox botched to a Ford engine taped in a Volvo chassis does not make for a good car.
It sounds like I was wrong about the TSC when you are not on 36W, my memory of this is a bit hazy as I don't use my GM36 much these days. From what you say it seems it reports all 4 valves all of the time no matter what the power soak is set on, (which makes sense). My apologies for misleading you like that. That would mean that the original problem is now understandable. With 3 out of 4 valves shut off by something, (perhaps the TSC for some reason), the amp could not give you anything like its normal action so it shut off all sound. Though it seems to be working now there is something I would do when you get a minute before you rely on it.
If you have any special voices programmed in, back these up or at least take written copies of the full range of their settings. If you haven't got that far yet that's no problem. Then do a factory reset of the software. This needs no equipment or special downloads. It will purge the amp's software setup and reset everything back to original factory spec. That's not just the voices, the firmware in the amp's digital systems is cleansed too. Sometimes, (not often but we have seen it here a few times), you can get corruption in the driving software which causes odd effects when that area of the programme is accessed by the amp. It would be good to know that your software is pristine without any of those bugs hidden away and waiting to pounce.
The procedure for a factory reset is in the manual in section 8.3. It's easy, just press "Store" and "FX Access" together while powering the amp up with the Power/On switch. Both buttons will flash three times to indicate a successful factory reset. I do stress, copy any personal voice settings first as these are permanently wiped along with the firmware.
Do keep in touch with us and let us know how your new valves get on. If you have the original Chinese valves in there you may notice some difference but I really wouldn't expect miracles in tone. This is subjective however and some people rave over the minutest differences they can detect, (or at least they think they can
). For my money there are other factors which change with each playing venue which have a far greater effect on tone and wipe out any subtle changes a valve type may make. I stress again. There IS absolutely NO difference between valve makes caused by frequency response factors. ALL 12AX7s which carry that model number MUST conform to a flat frequency response into the MHz region. Any genuine differences come down to different overload characteristics which is driving the valve beyond its design capabilities and out of the area which the valve's designers try to control. The people who blather on about one make's top end or another make's solidity of bass are talking out of their asses! When they make their test comparisons they always have the amp set so it is heavily into their favourite distortion region and that is what causes some to sound sharper or smoother. Turn the amp way down into the ultra clean linear region and take an honest listen then. Of course engineers can show this easily with more sensitive equipment than anyone's ears, but hey, don't let the proven truth get in the way of a good story. Or a good income?