MacBook Pro (Mid 2009) Turns on Intermittently

I've been having problems with my MacBook Pro lately. The biggest being that I can't turn it on. I took it to Apple twice, and both times they reset it by taking the battery out. This works for a day or two, but then my computer goes back to doing the same thing. I had to reset the System Management Controller to get it to turn on again. They told me it could be the power cord, which I checked, but it is not frayed anywhere. The computer once turned on will stay on for a long time (I backed up the hard drive for 6 hours, though it did turn itself off after). I replaced the surge protector I plug it into at home, to no avail. I'm not really sure what it could be. When I try to turn it on, I will get either a white or black screen, and then a clicking sound as it shuts off. This past time, the screen was not at the correct brightness as well.

Here is my computer's information:

15 Inch Mid 2009 MacBook Pro

Processor 2.53 GHz Intel Core 2 Duo

Memory 8 GB 1333 MHz DDR3

Graphics NVIDIA GeForce 9400M 256 MB

Software OS X 10.9.4

I had to replace the hard drive 2 1/2 years ago with a 250GB Western Digital. I upgraded the memory to 8GB last year. Right now, it seems like the only way to get it to turn on is to reset the SMC every two days, which doesn't seem normal. What else can I do? I don't want to take it back to Apple, they don't seem to know what it could be. I did try unplugging it, hitting the alt + command + option button and plugging it back in, waiting, and then trying to turn it on, but that didn't work. The resets work, but not for very long.

Thank you for your help or suggestions.