I've actually had a remarkably similar experience over the past year or so (Except the smoking part). Personally, I'm pretty good at fixing my own computer parts, but my computer has been an uphill struggle from the start, which happens to have been about three years ago as well. It has always had freezing problems related to the motherboard/CPU combination, and when I just gave the hell up on it a while back, my dad exchanged the motherboard for another, didn't care that he got a completely different model altogether, and found out that for some reason, half of its processing power was being spent doing nothing. Long story short, my motherboard is half-dead and only continues to work at (relative) full capacity because I disabled over half of its optional components. I also had a HDD failure, but I literally heard it coming, and out of sheer I-don't-know-if-you-can-even-call-it-luck, I had a spare HDD lying around that I decided to back up files on for shiggles. I also got a terabyte drive as a replacement, and I had already been running XP64. Then my dad just randomly handed me a RAM upgrade, no questions asked, 'cause something he had a question about started too slowly on my computer. Then my GFX blew capacitors 'cause it's a crappy commodity card that I'm overclocking as far as the software will allow, but I happened to have more than one dead 360 lying around (!!!) with just the caps I was looking for.
... So, in order to actually answer your question: Under similar circumstances, I don't have the option of spending any money at all on the problem. You do, even if it's limited. I'm assuming that by Intel dual core, you mean that you have a Pentium D, in which case, I've seen some fantastic motherboards for Intel+nVidia systems featuring a Pentium D for under a hundred US dollars. I'd say that your processor should last longer than you think, so just replace the motherboard.