Pick up a new coin battery of the correct size at Wally World or someplace. Cheapest way to test if that's the problem.
The battery charge holds the BIOS settings in CMOS. If it is weak, the settings can change. Just one bit changing can cause the system to not boot. Resetting the jumper or 'resetting' the battery will force the CMOS settings back to default. That will allow a boot. If the battery is weak, those settings will eventually change. Then, no boot next time.