Grey screen on HP Notebook - impossible to boot

I own a HP Pavilion dv9500. P/n: RL653AV.
S/n: CNF7293F7Q.
I bought it a year ago, any warranty I ever had had expired.
So, about a week ago the screen started to change colors like the graphics card crashed or went into thermal shutdown.
Since then, the cooler started to act out weird, and I'm guessing there were some heat problems.
After that, at every reboot, it started showing a grey screen with random black stripes, which slowly fade to an not uniform shade of grey.
I am sure that the OS is fine and there are no software problems, because, even though I can't see anything on the screen I can hear all the BIOS sounds if I enter BIOS and all the Vista sounds if I don't touch it at all. Keyboard and everything is working fine.
My guess is that my Nvidia card crashed and must be replaced, but, to be sure I want to connect my notebook to an external monitor.
My question is, how do I connect to an external monitor "blind" ?
I'm thinking this could result also from some loose connection between the monitor and the chipset, but, I'm thinking if this was the case, the grey color would be uniform and wouldn't fade at all.
also...
My second question is, could this behavior be associated with some other kind of hardware malfunction?

Thanks
Leni