Desktop Computer faults can be numerous.

No video signal

No sound

Faulty memory

No power

Fauty operating system

Viruses / Trojans / Spyware

Operator initiated errors

conflicting software

Corrupt registery

The list is endless...

Motherboards CAN be repaired.
Basic problems are due usually to the capacitors on the main board leaking due to excessive voltage from cheap or overdrive powersupplies.

So if you want to keep your motherboard and not have the expense of a new one, then repair is an option for you.