You are correct, you need Processor / RAM / Graphics card as a basic to get something displayed. In the older days you had to have a load connected e.g hard drive otherwise nothing would happen.

To me those beeps sound like 1 of two things, either the RAM or the graphics card, if the beep happens instantly as soon as you turn your machine on then I would suspect the graphics card.

See if you can borrow one out of another machine to test before purchasing a new one.

Every time ive heard that sound the CPU has been dead, apart from 1 time when it was CPU overheating.

I know this is kind of late but if you have not got an answer yet here is your system bios beep code

Repeating beeps Memory Error - Memory is either damaged or badly seated
Repeating Hi/Low Beeps Damaged or Overheating CPU