Do you have a high-frames config?

Try to have the task manager open in the background when you're playing and then checking it when it stutters to see what's going on. I have a feeling it could be some power saving features for your cpu, you could try going in the bios and seeing what you could find.

have you set your power plan to performance?

Please make sure you're running tf2 in fullscreen. laptops tend to throttle everything and use motherboard gpu on stuff that's not fullscreen.

[...] then dont expect better perfomance if you cant bother doing simple things

[...] I'm not gonna bother formatting and reinstalling everything just for one single game, I dont have time for that. There should be an easier and more logical solution than that (if the problem is in fact my computer and my settings, and not just Valve being Valve).

I'd recommend a reformat mate, and install steam and tf2 + drivers, nothing else, do a stress test and see what fps you can get, you doing all tweaks to recover your HD and generally your PC isn't enough tbh dude... Once you've done that if there is no improvement you have your answer...

[...] everyone did;_;

The 2.4Ghz shouldn't be such a huge problem. I ran a dual core pentium 2.7 Ghz, and managed to get 50 fps min on mid fights in 6s and never go below 60 at all other times. Rather than getting stutters, he would just get lower framerate. Do an antivirus check, before I had games stutter because of a virus... Also, can you replicate the results in other games? I would try a range of stuff. Something light like quake and maybe something more intensive.