I think you are right. I have the same machine and it has the same problem. My case is a bit different. When my Mac first behaved that way? I followed up and found that my LVCD fuse blew and so I had to buy a new fuse. I did this twice and still the fuse kept on blowing and so I decided to short with a wire. this time round the display worked for some times and went off when the machine warms. I've been thinking the problem ever since and I think you are right. it can be a capacitor issue. let me try to see if I can find the capacitor itself