Laptop after overheating occasionally doesn't boot

Hi guys! I got a peculiar problem with my 7 month old Lenovo Thinkpad E540. I know, consumer Thinkpads are shit, but budget was tight. Anyway, my problem - after a shutdown due to overheating (Ubuntu didn’t shut down properly and it was left running in a bag for several hours) it occasionally refuses to boot, even to BIOS. After I press the power button, screen backlight kicks in, but the fan won’t, no beeps and nothing happens. I then need to remove battery, pull out CMOS battery, wait about a minute while holding power button (supposedly to get rid of any power still in the motherboard) and then plug in AC-only and press power button. Any ideas what might be the problem and how to solve it? I’d really rather not suffer the RMA hell and I cannot imagine being 30 days without my laptop.

Thanks in advance

I'd take the back off and check for fluff & dust. You might consider getting a laptop cooler too.

It doesn't overheat anymore and it is as clean as it possibly can be. The problem is, after I shut it down normally, it occasionally will get stuck before even BIOS can kick in.

You could try checking your Hard Disk for faults. Also boot into recovery mode to check for broken Ubuntu packages. SuperGrubDisk is a handy tool to have around too, for boot failures.

http://www.supergrubdisk.org/

Possible useful link.

Link: http://www.howtogeek.com/196740/how-to-fix-an-ubuntu-system-when-it-wont-boot/

Not a hard drive fault. When that happens, my system wont even get into BIOS. Last time I checked, BIOS was not OS dependent, nor stored on hard drive :D. Either way, this problem occurred before AND after switching HDD for SSD.