It's actually a *very* unique computer. Known as the 350 (which as a result has some similarities with the PC 340) it was the first of the PC 300 series to have the "GL" suffix. I would like to remind everyone that the 6282 300GLs or PC 350s were designed just before the ATX was in full effect and were also very early machines to sport USB and optional onboard ethernet. So it is totally expected that an AT power supply would have been used as development most likely happened in 1995. In fact, the 6282 is IBM's first Pentium 1 machine capable of running 233 Mhz Pentiums natively.
The PC 300 that was released a year *later* does use ATX, it's the 6562 300PL. It also used the updated Triton II which meant EDO DIMMs exclusively-- unlike the 6282 which could use both SDR and EDO DIMM modules.
Another thing not mentioned is that the optional front 80mm fan uses a proprietary two pin socket-- although I would recommend just using a standard fan with a molex adapter if you're using a CPU faster than 166 Mhz (apparently IBM was confident that the giant socket 7 heatsink was adequate for passively cooling 166 and downward). Also the diagram on the internal lid states "VESA FUTURE" instead of "VESA FEATURE", clearly VESA wasn't the future...
If the PSU in your 300GL 6282 is dead, I would advise purchasing a FRU replacement-- or you'll have to open it up and troubleshoot what component failed. If you want one with an ATX power supply, get a 6562 or its brother in a tower form factor, 6592. Reworking the power supply with an ATX will be more problematic as AT power supplies are hard switching and not soft switching.