Computer problem please help computer won't turn on ?

If your computer didn't have the power connector, it isn't needed... there is an extra 4 pin connector for motherboard that require power or an attachment from it. The beep at the beginning of your boot process was an indicator of POST(Power On Self Test). During POST the computer test, the processor, the video card and the memory. Based on the fact it came on with you using another power supply, I do think the power supply was one problem, you may also want to check if u have the voltage switch on the right side(115V U.S. 330V International). Otherwise, since it shut off, I'd ume its a memory or processor problem. I'd check if the processor burned out or remove a memory module and/or replace it then try startin up the computer.