I resurrected my 2007 24' iMac last year, but it was just a bad HD (and I had a time machine back up). Actually the DVD had stopped working as well, and despite sourcing an original, it still doesn't work.
Opening it up and putting it back together was a bit of a PITA - and in some cases needed a helper - but the parts cost was low (just a $100 for a HD). Felt nice not to toss it for just a $100 investment. And I'm using it now to type this.
But if your's is a case of a bad power supply, getting the part + more than anything the time investment may not be worth it. A replacement used iMac, macbook or mac mini can be had for just a few hundred bucks. And if you have a time machine back-up, you can be back on your feet in an hour.
I think the probability some evil doer is going to rifle through your HD is low. If really worried, put the iMac on a large garden trash bag, take a hammer to it & the HD, and dump at your local county e-waste facility. $50 for it is not worth it, not for the security risk, but the time waste in the transaction.