"blew out its processor" is not very specific.
What exactly is and isn't the unit doing? Is there any video output (including a blank output, just essential sync signaling)? Does the optical drive still have power (open/close at least)? Is the relay still clicking when the unit is turned on? Has the power supply been tested in any manner to ensure it's still working (keeping in mind the fact that the originals are notorious for being failure-prone junk)?
There are at least four processors as far as I remember. The ASIC's exact function was seemingly never replicated, Bung is long gone to provide any info, and to the best of my knowledge NEC (who made that chip for Bung) never published any info about it. The chip can overheat and die. Some units have heatsinks on it (passive cooling, no fan), some don't have a heatsink at all.
There's also a chip for MPEG processing for the VCD support. The display signals may have had to pass through it, I don't recall. Is gets very hot, could fail, and would be difficult but not impossible to replace.
There's a Famicom/NES-on-a-chip processor. That shouldn't be very failure-prone.
I think the last one was a line/text graphics chip. It may have been the last stop in silicon for video signals. I really don't remember well. It doesn't seem likely to be a point of failure. It should be the most easily replaced processor in the unit.
Then of course there's the flash chip with the firmware. If it failed or is corrupt in some way that could make the device seem dead.
Lots of other possibilities of course (other smaller components, possible solder issues, and on and on...)
That's most of what I remember. A place to start maybe?