The beeps are quite important... They will differ depending on what motherboard and BIOS is in your computer... but they tell a lot.
Most often, beeps relate to Memory or the Video graphics card, but can be as simple as a cable that has worked its way loose, dirt and hair on the cpu fan or elsewhere causing cooling issues.
Any failed or failing component can cause the computer to shut down.
First, I would open the case, and look toward the center of the motherboard for a brand or model number. The maker of the board may also be posted on the edge... Or just tell us the brand and model of the computer... and we can help you track down the beep codes.
Listen very carefully for the beep codes that occur from a cold boot... We need to know how many short and long beeps, and the order in which they occur. Write them down until you get them right.
Post them here.