Hard disk problems usually should not prevent machine from displaying picture because the first thing the machine loads is open firmware and only after that it will start to figure out where it should boot from, but of course failed hardware can cause all kinds of symptoms.
It sounds like capacitor or graphic chip issue. If you have a model which does not have camera, then it is very easy to visually inspect capacitors. Just put it on table display side facing down, you might want to put a towel or something under it to avoid scratching the frame:
http://www.macwiki.nl/images/e/e7/Imacopschonen4.jpg
There are three screws which you need to open, they don't come off. After that you can lift and remove the back over. After this you can see capacitors and if it looks something like this:
http://www.instructables.com/image/F6WK6L2G3TDN8SZ/The-Imac.jpg
Then you know where the fault most likely is. Models with camera (iSight) are built differently and are not as user accessible. iFixit.com provides instructions. When you have the back cover removed, you can also pay attention to those diagnostic leds when powering up the machine:
http://support.apple.com/kb/HT2831?viewlocale=en_US
Most likely you have first two when there is no picture and third when there is.
If it is solder fault then it most likely needs a professional to repair. Chips are attached with tiny balls of solder which sometimes crack after continous heating and cooling cycles. In new machines ("new" meaning machines made during and after 2005 or 2006, can't remember when the RoHS thing started) the solder does not contain lead which makes solder material bit flexible so it can tolerate those heat -> cool cycles better, in those cases the proper fix is to replace (reball) that solder with one that contains lead. Here is picture of my Intel iMac's ATI chip which has been reballed:
http://aijaa.com/0090610403668
Easier but more unreliable fix to reflow the chip back which basically mean heating the chip enough to cause the solder to melt and reform connection. It is unrealiable because it still contains that same solder which already failed once. Sometimes it is the chip that actually failed, but most of the time it is only the connection with motherboard which has gone bad.