|I never had good luck with emulation, but then again my computer is old as shit...
Is it running DOS ?
I remember using NESticle on Win98 and having a stack of floppy disks with NES roms on them. Right now I have a laptop with 2GHz dual-core Athlon and 3GB RAM with garbage on-board GPU that can run Gamecube games 'fairly' reliably. Everything prior runs fine, so even a dirt-cheap computer can run all the old stuff.
The only problem with emulators is that they're hacked together to make as many games as possible run as smooth as possible, so games that used hardware tricks to achieve things won't work correctly in emulation. That kind of thing is most apparent in Saturn games. And some NES emulators won't have certain mappers
and you have to find one that emulates the specific one you need for certain games. This site
has a list (outdated) of what emulators have what mappers. It's been a few years since I played a game that used esoteric mappers, so FCEU or Nestopia might actually cover most of them now.
is a good list of mostly-up-to-date emulators.