iMac has black screen - won't turn on properly

I've tried resetting the PRAM and SAT but that hasn't helped.

After watching a movie, my computer froze completely, so I had to hold the power button down and restart. I can still hear the startup chime when I restart it, and the keys make a sound when pressed. The white dot on the front panel is lit. However, the screen remains black (no, it's not the brightness - the screen looks completely turned off).

It's a 17" Intel iMac from late 2006 (Tiger era). It's currently running OS X Version 10.5.8.

Yes, my beloved iMac is rather old but it has been working just fine lately.... Although it wouldn't be surprising if it's a hardware failure. It's been used on almost a daily basis since I got it. My hard drive was replaced not too long ago, and based on what I've seen from other peoples' issues, I don't think it's a hard drive problem? (At least that's what I'm hoping, because there are some files that were still in the process of being backed up.)

So, what else can I try to do to fix my mac? If all else fails... I could use some advice on how to transfer data from my internal HD to something else. Unfortunately, if it's a hardware failure, I'd probably be better off buying a new machine instead of replacing more parts (while I'd love a new mac, I cannot afford one right now).

I'd appreciate any help on this.