Sorry to hear that. IANAD, but two possible (but money eating) changes that might help:
Buy an LCD monitor. LCD monitors can't flash quickly like CRTs. Might help, especially if the LCD isn't too top of the line.
If your computer is < 1 Ghz, buying a new computer might help for many of the games. However, if the original game flashed like that, this won't help.

I'm sure there's software ways, too, but that's out of my league.