That can be tricky. It's pretty rare for CPUs to die but from the ones that did in my case they all failed to produce any BIOS beeps. The best way to check is to remove the suspected dead CPU and put into a known working motherboard. If it doesn't POST then it's probably dead.
i think my cpu dying because on 3DMARK06 the graphics tests are good but when it does the cpu it's real chopy like two seconds between frames also on nascar 2003 season whhen you get in a big pack of cars it slows agit not alot though now on call of duty 4 it's ok but when thair's a bunch off stuff going on at the same time it slows real bad.
All but quad core CPU's do 0 to 1 frames per second in 3DMark's CPU test. That's because CPU's are lousy at rendering graphics, but some of the quad cores can get 2 or 3 frames per second. I think the CPU tests in Vantage are a bit more reliable (but that requires Vista and it's no longer a free benchmark).
You didn't mention your graphics card. I bet that's the problem. Turn down the resolution on your game and you'll get better framerates.
1.) To have another CPU that can be used in the socket.
2.) PC speaker beeping codes for bios, if video card doesn't show POST on the monitor.
3.) Have some kind of PCI Post DIAGNOSTIC Test Card that displays codes to trouble shoot.
4.) or if your MB has some other way to diplay error codes.
For example, my MSI has what's called a d-bracket. It fits in a slot, hooks up to a header on the MB and displays 4 led lights (red/green) to indicate any potential problems (CPU/RAM/ect), rather then just system bios beeps from a speaker.