Just 2 make it simple, I am assuming Your monitors along with cables 2b ok. can You test Your GPU elsewhere please? it may be tested in 1 of Yours friends PC, 2 say.

It doesn't sound good. The lack of beeping and what you said about rebooting leads me to think there's a problem with the mobo.

Did this start randomly or directly after using a second monitor?

Do you hear anything out of the ordinary as the pc starts up?

The PC sounds like it's booting up ok; I get the usual bling etc to denote it's up and running. I've swapped out both cables and have even tried the DVI with a display port adapter. The monitors are both new. I've tried it with just the vga and just the DVI.

And it just started with the introduction of a second monitor

Well, I got the PC from a mate who swears he didn't have any problems with it while using a single monitor

Well I cant say for sure but if the monitors are new and work with other pcs, then the problem has to be the gpu or mobo.
Have you tested the pc with a fresh monitor? It could also be related to the set resoloution not being supported by these two monitors

No, but they do work occasionally so wouldn't that suggest that they're supported?

If they're working then yes, what I'm suggesting is your system is set to a resolution not supported by either monitor...but I've just realised you should see the post uf nothing else.