'95 5S-FE Randomly Shutting Off Options

[Chockomon]

Hey guy, I'm not too familiar with Celicas as I'm more of a VW guy, but I would love some help on some issues I'm trying to diagnose. My friend just bought a 95 GT convertible. The engine runs great and it drives amazingly. However, it has this random stalling/shutting off issue and I can't seem to figure it out. Here's what happens:

The car will shut off out of nowhere. Doesn't stutter, shake, no CEL, nothing.
It happens at any time, independent of temperature, weather, engine temperature.
Usually will turn right back on as if nothing happens.
HOWEVER, sometimes it will not turn back on. When this happens, no CEL or battery light (warning lights) will turn on when the key is turned to the on position.

So where do I start? I'm thinking that the issue could be a faulty relay but I don't know which to look at / ring out. Could it be the Main Engine Relay? EFI? How would I go about checking the ECU on this car?

Thanks guys!

[Chockomon]

Battery terminals are clean, battery was recently replaced with a DieHard Gold. Plenty of cranking power, never needs to be jumped. Usually, the car will crank, start and run fine until power just cuts out suddenly. It will either then start up again like nothing happened OR it will not crank. When the no-crank issue happens, the check engine light will not turn on when the key is turned to the on position.