Hooking up a different PSU to your system won't pose any harm. When you connect it, if the mobo LED glows, you'll likely have your answer then.
If the PSU blows, it may not even have standby power.
CPUs are pretty durable. They don't normally die like that. If the PSU blew, it could take the mobo with it. The easiest way to find out, is to try a new PSU.
Cheap PSUs can blow at any time. What kind is it?