Memory bad, Hardware Conflict, CPU problem, CPU FAN, Overheating, video card failure, shorting
Memory: A bad stick of memory can causes beeps along with not starting
Hardware Conflict: 2 of your hardwares are conflicting with each other, preventing the computer to start.
CPU Problem: The CPU has not been installed right, backwards, or has not been pushed all the way down.
CPU FAN: On some motherboards if the CPU FAN is not spinning at a certain RPM, or is not spinning at all, the motherboard will beep a warning and turn off.
Overheating: Your Heatsink has not been installed right, and is causing overheating and causing shutdowns.
Video card failure: Your video card is dying or dead. If it is integrated or onboard then its RMA time. If its an expansion type, it's replacement time.
Shorting: The motherboard is touching the case, causing it to short. If this goes on for periods of time your motherboard and CPU may get fried.