My laptop is 4-5 years old. I had to restore the system using Ctrl - F11. I was using the laptop with electricity due to the laptop not working when the battery was installed. I am cruising on the internet and the system just phizzes out, power off, black screen. I wait power it back up and it takes me through selecting a user account, the windows scrolly bar thing and takes me to a blue screen with dell all over it, maybe the Dell welcome screen??? Anyway, there is sits; no hourglass, no fans, no nothing complete and utter silence. I have tried F8, F11. The screen seems kind of erratic also, kind of there not there. I am very aware that I hear no fans - not sure why this sticks out to me???
:^/ If you're getting to a login screen, then the system is intact enough to find the hard drive and boot from it. So, perhaps it's not beyond repair. If the fan isn't working it may be due to a faulty controller for it, or a change in whatever settings govern the fan.
In your place, I'd remove the hard drive to another PC and salvage whatever files are important to you. Then I'd put it back, boot from CD or floppy with a BIOS upgrade and try that. (Flashing the BIOS might restore any corrupted data, see.) Then re-install the OS, etc.
On the other hand, if the controlling circuit for your fan is fried, and your video card is generating wonky data, then it's likely that you've sufferend other damage as well. So, you may be out of luck, but it's worth the effort to repair/restore things just in case it works....
;^) Just make sure to back up/salvage what you can first.