You said that you swapped RAM already; have you also tried removing non-critical components (CD-ROM, network card, etc.)? If that doesn't yield any positive results I'd suspect a motherboard problem or a weak power supply.
Try a BIOS reset. There should be a reset jumper somewhere on the mobo; check the mobo's documentation for specifics. You can also force a reset by unplugging the computer and removing the CMOS battery on the mobo. Leave the battery out for 15 minutes or more before replacing it; it can take a while for the residual charge to dissipate.