IF you don’t have virus’s and spyware etc. run CCleaner (google it) Make sure your Hard Drive is not full. Delete programs you don’t want. Invest in an Solid State Drive. (Best thing for ANY PC if its HDD) A no moving parts hard drive speeding up start up/shut down and overall PC tasks. Chances are you had enough RAM (Memory) all this time, it isn’t going to help you much now unless you decided to Edit Video etc.
As far as the mouse and keyboard go, its bluetooth. The OS has to turn on the bluetooth. You can’t get past stages of boot. Sounds like you need to reinstall the OS. Buy a new battery, you can find them in any drugstore. CVS. $3? The boot menu doesn’t seem to be correct and the PC is asking to restore. Use a wired keyboard for now.
Take the hose off and tape one end up, fill it with water. Fill the tub and dunk it in pull it out… If it leaks, you got a hole. Completely dry before using it as it has electrical wiring in it.. basically the ends need to be completely dry.. if the hose is not damaged, if I remember the ribbing on the hose is the electrical wiring. The top where it plugs into the metal rod of the power head it twists to tighten it? A used hose from a vacuum cleaner repair shop will cost ya 25-35. The vacuum cost me around $350 every time I bought one, lasted 2-3 yrs. I use a Shark from Target now. (Costco sells them too) Cost $175. Amazing how much dirt it picked up after I just vacuumed with my Kenmore Canister. slickdeals net
If you can’t unlock the screen because you forgot your password to it, that is a security issue. So you can call Apple to have them tell you the procedures to reset that. If it is reported stolen and locked, nothing you can do.
"I hit the breaks to stop at a stop sign and all power went off." A wire harness was near or under the break peddle as you pressed it down and it pulled wires out the back of the gauges. ( sounds good to me ) Could be simply easy to just lay on your back with a flashlight and look up in the area behind the dash to push it back on. "I also have a leaky a/c problem that I need to get fixed because I live in a very humid state" You have more issues to fix before dealing with your AC. You need to go to an AC guy to do that troubleshooting. They can put in dye to find leaks and sniffer tools to detect leaks in the AC system. Sometimes it can get costly. Sometimes its just a simple filler valve tightening and freon.
The extreme are known for battery issues, there are plenty of videos on how to change the batteries in it. I suggest you change the batteries. iFixit might even sell the batteries /shrug. U Tube for the win.