Windows XP - Intel Celeron D Processor, 512MB, 80GB, CPU 2.93 GHz, 504 MB of RAM. with DirectX (I can emulate N64 and PS1 games without a problem). My graphics card is listed as "Intel(R) 82845G/GL/GE/PE/GV Graphics Controller".
The CPU is probably the bare minimum you can get for this emulator[I had a single core P4 3Ghz and it ran games decently but not full speed]. And that ancient integrated card needs to go. Get yourself a nice Geforce or Radeon instead. Just about anything from the GF 6-7 series will suffice[I had a 7900GS and it ran the games fine]. As for Radeons, not too sure. Anything in the X2000 series or higher I think?
At the least I'd pick up a real graphics card. That should give you a good boost[not incredible if your CPU can barely keep up, however], but keep in mind that emulation will always be more CPU based than GPU based.