I can't boot my Mac anymore

That's pretty much the problem.

You see, it's an iMac from the Late 2007 If I'm not mistaken. It's pretty much the third time I've had to renstall the whole software, the first time for unknown reasons and the second because everything within was deleted, out of the blue.

This time around, I'm told (by family at home) that the computer froze, and they used the safest method to turn it off, a.k.a. Press the power button for several second until it turned off. Ever since it didn't boot anymore.

I press the power button and THE flashing folder with a question mark pops up after some seconds, and that's pretty much all I can do. I've tried booth in Safe Mode (with Shift), booting in Recovery HD (Command-R) and even tried Startup Manager (Option key), but i only get a floating cursor and nothing else happens. Literally nothing else happens.

I thought it was the HDD Finally crashing, so I left it alone for some time, and incredibly the next time I tried it booted perfectly. As if nothing had happened. But it froze again, we had to power it down as mentioned above and this is my third day trying. No success except for that bit of magic.

Now, the Mac doesn't really have any important information anymore, and I don't have a Time Machine backup either, but it'd be nice if my files didn't erase this time around. To be honest it sounds like the HDD finally died, but again, it booted normally after one night, sadly not anymore. I personally have my suspicions on the cable, but I'm not the expert.

Any help? Thank you in advance!