So, here's what I'd like to do. I'd like to run a few PC fans to cool down my laptop, because it's a HP and its cooling sucks (actually it doesn't, my laptop would be cool if it would suck). I need to power them somehow obviously, and since they require 12V and USB is only 5V, my dad, who is an electrician says it wouldn't be smart to hook them up to a USB.

I do have an old 300W PSU which has been sitting since the birth of Jesus so I'm not sure does it work, but it was in the box all the time and it was replaced for being too weak and not for dying so it should work.

My question here is, would it be possible and safe to run fans with that PSU, considering that I somehow have to override the power on mechanism and the fact that there won't be a PC hooked to it? Oh, and I guess it would only use as much power as the fans use?

PSUs are very unefficint for running just fans. PSU without anything hooked up uses takes alone 10-15 W, + there is noise from PSU fan and that buzzing.
Since fans use relatively low power 1-2 W, you are better of using some old router/switch/whatever adapter. Even tho fans are declared to work @12V, they work just fine @5V (bit slower)...

You can get pads under a laptop so it has space to intake air and there are pads that have USB 5V fans. I have them but don't use the fans, they work great though, I can use of the two 80x10mm fans and unplug the internal loud laptop 52mm blower fan.

You can run 12V fans from 5V too if they will spin up, they just won't push much air. Usually fans take 0.2A at full power.
Theoretically 1 normal 12V could run from USB2, the power is there.
USB3 probably has even higher power limit.

Well, I have raised my laptop so it has more space for air intake, but it doesn't help much. A friend also borrowed me his laptop cooler and it only worked if laptop was at least 3cm above the cooler, it had no effect when the laptop was sitting on it or when it was just slightly above the cooler. That's why I'd like to put some larger fans to get air all over the thing.
A friend of mine also has a laptop similar to mine (mine is a HP g7, hers is a g6, the difference is in the CPU and the laptop size) and she also had cooling problems but her fan died and when she got it replaced the laptop started working like a charm, but I do not have enough money to do it right now so I'm trying different solutions.

E: The biggest problem is that the laptop has no passive cooling at all. I was thinking of buying one if it exist and putting it inside the laptop, but I'm not sure if anyone even makes these since the laptop originally doesn't have one.

EE: And thanks for the info about the fans.

Laptop overheating is caused by:

1: Dust clogging the inside, blocking airflow
2: Broken fans

Open the laptop and remove the dust. Replace any broken fans.

I opened it. There was no dust inside. There is only one fan and it is working.