Need Help ? Starter/battery/solenoid Prblems ?

I recenlty tried to start my car (1998 Ford Taurus - Automatic) and nothing happend. It was like there was no battery at all in the car. Once jumping the car, it started immediately. I checked the battery using a volt meter and it read 12.95volts which should have been strong enough to start the car. Correct? Well after that I disconnect the wires to the battery and clean the posts and the terminal connects (and ground too). Still nothing. Then I checked fuse and everyhting seemed ok. NExt I noticed that the Mega Fuse block under the hood had some corrosion, so I disconnected the wires and the fuses and cleaned up the connection here. I'm not sure if I put everyhting back together in the correct order. There are three wires and one fuse. Does it matter what order they go back on in??? Next I disconnected the "starter & selanoid" and took them to the parts store to have them checked out. They both seems to work just fine. Next I switched out the battery with a battery from another car (kinda old but still ok) Now the car kinda starts....The starter sounds like it's just spinning. Do I need a stronger battery or did I just miss something when I put the wires back on the mega fuse or the starter/selanoid???

Please any help would be appreciated.....I cannot take being locked in the house another day without my vehicle.

thanks in advance !!!