Your laptop has a fan for a reason, and it's not to cool your lap... It's not a lint removal tool either but that's a job it WILL DO well. Suck up enough of this lint or that cat hair and your fan will fail to cool the temperature sensitive CPU. If your laptop only has one fan, consider your video card a close contender in the race to overheat, stall or shut it down. How long does that take?
... Just a few seconds.
How can you tell?
1. Look for the air intake holes/cooling fins on your laptop. Hint: It's not supposed to look like carpet (plugged with lint or debris).
2. Use your nose. If it smells like toast.....it probably is.
3. If you used to hear a fan during startup but don't anymore, stop trying.
Salvageable? Maybe
Invest in a "can-O-air" - blow out any obstruction in the intake cooling passageways. Get a straw and go ghetto if you must because the human mouth can blow up to 7psi. - that's enough to make a difference (warning; it's also enough to make you faint like a Southern Belle).
Short on time and breath? Take it in and get it cleaned out and replace the cooling fan too (an inexpensive assurance).