I'm no expert in this field, but it sounds like some critical chip on your PS2's mainboard is failing (Expansion and contraction seems to affect the connections inside it, and hence causing failure).
When it boots (sometimes seldom, sometimes often), I can play games just fine. But it's a matter of time until the picture freeze, then the sounds are looping. When I turn the PS2 off after that state, it often won't turn on. Then we're back to the start, no picture. It can also freeze in the PS2 main menu, even with no disc inserted. At first it came to me that it was overheating issues, but this can happen after 10 minutes of playing. Even when the temperature is cold in the room.
I've checked the modchip installation several times (checked for almost-shorts and dried solder-joints), and looked through the motherboard for any suspicious stuff. Nothing... Can it be the PSU?
This problem is different from overheating (Your console should still work in that case, provided that it didn't suffer damage from overheating), but is similar as your console's parts don't work properly depending on the environmental temperature (The internal connections are affected by expansion and contraction).
PCs are also prone to this problem, and is usually caused by aging (You can see some old, 7-10+ year old PCs having erratic issues, like certain parts not functioning properly or not detecting some parts).
Sorry, but unless you can find out which chip it is (It could be even the EE, hence your PS2 doesn't boot) and replace it, your best solution (And most permanent one) is to replace it (Other chips may fail eventually).
You have not experienced any power surges?
SCPH-10000 S. MINOKAMO v1.01 (Defunct)
SCPH-10000 S. KISARAZU v1.00 (faulty)
SCPH-15000 S. KOHDA (With warranty seal!) :D
DESR-5100 S. EMCS