Can you remember how many beeps you got when it was making a noise?.........was it more than one?

I suspect that a basic machine like e-machines probably uses onboard video. If you have an old PCI video card or can borrow one, that would be an alternative to r3b00+'s suggestion.

Can you remember what colour the HDD light was when it worked?

Partial failure of the motherboard and/or power supply unit could cause this, but we really need to find out more.