You have some problems:
-The fan will not cool all the things that it may cool.
-The pc will overheat constantly (more than what you think)
The thing that you should have done is buy the exact part for your pc. You probably bought the incorrect piece (some extra fan of the same pc or a desktop pc fan).
If you will change the piece (you should buy the whole piece new) don't forget to put some thermal paste over the processor and the GPU (you need to clean the old paste and replace it with newer one).
And I don't recommend you to repair things without the necessary tools because you can mess things (I did that a lot of times).
Greetings, Koxx.