It's most definitely either a Power Supply or a Motherboard issue.
The Power Supply is a more likely candidate, especially because of the "leaving it off for a few months and magically working again turning it on afterwards" part. This can happen for many reasons... but an incident like this is likely to be Power Supply related in my experience.
I would suggest you try a different Power Supply to confirm this first... have you got a friend or someone that can perhaps lend you one to test?
You can also buy a Power Supply if it's refundable to test this out and return it later if it's not the problem.