Sony Vaio won't turn on...help!

I haven't used this site before, so I apologize if I posted this in the wrong place...

I have a Sony Vaio laptop VPCEH14FM that is just over a year old.

About 2 months ago it stopped powering on. When it's plugged in I will occasionally get an orange light to come on, but half the time that doesn't even happen. If the light does come on, I can get it to boot randomly if I just continuously press the power button for 5 or 10 minutes. If the orange light doesn't come on, then it won't power on at all.

If it won't power on, I can take my laptop apart, take out the CMOS battery for a few minutes, and when I put it back together it will operate just fine for a few days. Then if I change my settings to where my comp never turns off as long as it is plugged in, it will work fine indefinitely.

Regardless of whether or not the light comes on, I can get it to boot to my Splashtop Browser by pressing the WEB button on my keyboard...so it is NOT a power supply or battery issue because Splashtop Browser works everytime.

So if it's not a power supply issue, and resetting the bios by taking out the CMOS battery works everytime, what could an actual solution to the problem be? I travel a lot, so leaving it plugged in and never turning it off is not an option.

Thanks in advance for any solutions or help! And please bear in mind that I am not very tech savvy.