There are a lot of ThinkCenter computers made, what exact model?
Could be anything from a failed motherboard or power supply to a bad CPU to just a loose connection somewhere. Need full details about when this started and what you tried already if anything. Try a BIOS reset to defaults, unplug computer from power, remove the CMOS battery for about 10 seconds, try it again.
Also look over the motherboard for any issues with capacitors, depending on the age of the system, faulty motherboards can be common in some ranges of systems, especially if it's IBM branded since that will make it an old computer.