Why won't my computer turn on?

I have a late 2008 Macbook Pro. About two months ago, I shut the computer down and when I tried to turn it back on, it would not boot. I tried resetting the SMC. It did not work. I also tried a number of other suggestions I came across on the internet, such as unplugging the power cable, holding down the power button for 10 seconds, and then plugging the power cable back in. Nothing would work. A few days later, the computer randomly turned on after I held down Shift + Control + Option and the power button and released them at the same time. This had previously not worked.

Fast forward to this week. I, perhaps stupidly, shut the computer down. Once again, it will not reboot. When you press the power button, nothing happens. I should note that the battery indicator shows the battery is fully charged. Also, when plugged into the computer, the light on the magsafe charger glows green.

Does anyone have an idea of what might be wrong? Before this happened, the computer ran well. The only problems were the fans ran very loudly and the machine tended to get quite hot. I should also note that about a year ago I replaced the hard drive with a brand new solid state drive. I also replaced the ram with 8 GB. Finally, the machine has a new battery purchased from iFixIt.

Any help would be much appreciated. Thank you!