I think I just screwed up my computer

My computer was making funny noises, so I opened it up, took the fans out and took the big pile of dust out of it. I have done this several times, but now when I put everything back together and turn it on again, it hardly does anything. The fan starts spinning, but I don't get anything on the screen...

I think I just fucked up my pc...

So how're you posting this?

my work laptop

The CPU is not connected. Also I think you did not apply thermal grease between the heat sink and the CPU, which means that the CPU would get too hot, and the comp shuts down to protect the CPU. Your options are to extract the CPU and put it back ensuring all the pins are connected properly and to put a thin layer of thermal grease between the heat sink and the CPU before closing the comp and switching it back on

You probably dislodged a small wire when removing the fans. Most of these tiny things consist of very thin wires (often two together - one black on red) which end in a small piece of white or black plastic.

This gets pushed, like a small fragile crappy plug, into a connector soldered somewhere close by. Have a look to see if any of these are flopping around inside, near your fans.

You probably did.

Not a lot anybody can do without seeing it though.

Gosh, I'd be there wriggling my RAM well before staring at my CPU with a manic grin and a jar of vaseline in my hand.

This is known in the trade as "preventative maintenance". Maintenance prevents it working again...

The weird thing that I noticed, is that the processor is stuck to the cooling block... that means I can't lift up the little lever of the processor socket, and I just have to push it in with the cooling block all together.

The thermal grease is dried up and therefore the heat sink and processor are stuck together. You need to gently separate them, and put fresh thermal grease. The best way is to insert a flat head screwdriver in between and gently rotate it. If you are clueless, then first try and watch a youtube tutorial on "how to replace thermal grease".

Super! that was it I have replaced the thermal grease and put the cpu in it first.

Thanks for the advices!