If you invalid opcode messages running any kind of software, I suspect your computer has a stability problem, possibly caused by broken memory or cache RAM. You might want to run memtest86+, Version 4.1 or earlier (later versions crash on 486 processors), with L2 cache enabled and with L2 cache disabled. If you get errors only with L2 cache enabled, it is extremely likely that the cache (or the mainboard) is bad. If you get errors with or without L2 enabled, likely the RAM is bad, but it might also be due to the mainboard or the processor.
If your 486 processor runs at 66MHz or faster, make sure that you provide adequate cooling (at least a heat sink). If your processor is a 5x86 at 133MHz or more, you should also should have a fan. This is the bare minimum for stable operation. Please don't take the statement as "you are fine to run a 486DX4/100 without a fan". Intel recommends a fan on those processor for a good reason. But you can often get away for some time without - especially if ambient temperature isn't too high.