|Check with the manufacturer for documentation on troubleshooting.|
If there is none, might give this a go...
Remove everything from the mainboard; CPU, Memory, Fans, etc. All you want is the bare mainboard and power supply. Reset the CMOS to factory settings if possible. There are a few connectors that need to be connected - power on switch and speaker (not sound card). You should get beep codes when the power is applied. The codes vary with manufacturer. The code should indicate CPU missing or bad. Remove power. Install the old CPU with fan. The fan should spin when power is applied. Also beep code should indicate memory bad or missing, or bad CPU if it is defective (sometimes no code here is a bad CPU). Check the speaker to be sure it works. Check the voltages on the power supply while you are there. Low voltages can also destroy electronics (to much amp draw).
Personally, I buy a mainboard, CPU, and memory as a "set". Upgrading is not a bad thing. If it is an HP, Dell or other proprietary system, their board may be the only fit for the case.
This general troubleshooting information is the best I can do with the limited amount of system information you provided.