Yes laptops are a royal b*&^h to get into and reclose properly, but once you are used to doing it it's just like a desktop with more bother.
Those are actually ribbon cables connecting your keyboard and likely the mouse to the motherboard. Chances are, there is one for the LCD which is unplugged now.
As much trouble as it seemed to you that the laptop was to get open, to fix this you are going to have to get much more familiar with it. take the entire laptop apart, finding out where things go, what goes to what, and learning it like the back of your hand, you will eventually thank yourself for the trouble and knowledge. Once you get familiar enough you will find where each of those ribbon cables go and how to seat them properly... most of the connectors have a little clamp part that you pull up and out to one side before sliding in the ribbon cable, then slide in and down to lock the cable in place. A few of them do it backwards, where the little clamp is up while inserting, and gets pushed perpandicular to the slot hole for the cable to lock it down. A few of them have no lockdown clamp like that. and the cable just snaps in, but the plastic ribbon cables you have are definitely the mini clamp connector kind.
The laptop not powering up means not all the connectors are plugged in right, that's all. Learning where they all go will fix it in the process. 🙂 I wish I could come to your place and help, as I have much experience in laptops, but I doubt that is a possibility.
~edit~
Another thought, if you google your laptop model plus words like "Service manual" and "parts diagram" you may be able to find a PDF with instructions on disassembling and assembling your particular laptop. just a thought.
As for replacing the fan itself, that is not gonna be cheap but depending on where you go it may not break the bank. Sometimes the OEM will sell them, most of the time you gotta find it through searches on the net, a supplier that sells one either used, refurb, or new.