Thinkpad P50 won’t boot and has only Lenovo logo on screen.

SOURCE: IBM ThinkPad R52 Screen fades to black

Try using a flashlight at different angles and let me know if you can see a faint image of the desktop If so It is your inverter board that needs replaced.
http://www.google.com/products?q=IBM+ThinkPad+R52+inverter&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&sa=X&oi=product_result_group&resnum=1&ct=title

SOURCE: Computer wont boot. Gets a blue screen stop

you can try pressing f8 from restart of your laptop I am familiar -with this blue screen with writing /
hold down f8 from start up /option screen should come up select safe mode and press enter
when its in windows restart computer as normal
if this dont work /the only thing is to get someone to reinstall windows for you hope this help

SOURCE: IBM R52 laptop is getting stuck boot up

TRY AND REMOVE YOUR RAM AFTER THAT RESET THE MACHINE BY REMOVING THE SYSTEM BATTERY AND SHORT CIRCUITING THE BATTERY CONTACTS FOR 30 SECONDS MAKESURE THAT YOU'VE TAKING LAPTOP BATTERY OFF FROM THE MACHINE AFTER THAT PUT BACK THE RAM THE TRY TO SWITCH IT ON AGAIN

SOURCE: IBM thinkpad R51 won't boot

Sounds like at least a corrupted OS, but most likely a bad hard drive. I'd try reloading Windows (if that's your OS) first, which should take well under an hour; if reloading takes excessively long, then the system is probably having a hard time formatting the hard drive due to physical bad sectors and the easiest thing would be to replace it. The R51 uses good old ATA/IDE 2.5" 9mm height hard drives, which are not available in most stores any longer, but you can probably get the same size or larger ones on eBay for pretty cheap and replace it yourself. Expect to pay about 50 cents to 75 cents per gigabyte - anything more would be considered tourist prices...

SOURCE: Lenovo ThinkPad X61 got "thermal sensing error" when it boot up

OverheatingWhen the CPU overheats then it will shut down (i.e. thermaloverload) and won't boot up again until it has cooled down. If this is theproblem is not fixed then the CPU will eventually fail.
A faulty fan causes the problem or the fan and heat sink assembly are cloggedwith dust.
Check the CPU fan to see if it spins freely, if not replace the fan.
If the fan and heat sink is clogged with dust the remove the dust and make surethe vents are clear and dust free. Use a small brush and can of compressed airto do this.