Battery/Starting problems

Was at the gym, went to turn key and the power died, figured it was the NSS because ive had this problem before, mess with the stick a little bit and power will come back. Was having a harder time this time, so got a buddy to jump me and it got power and started up. On the way home every time id slow down to a stop the power would drain and the car would almost die. As i was pulling in my drive way, luckily, it died and i coasted in. Figured it was the battery so i switched mine with my brothers. Was putting on the connectors and was having a hard time because sparks kept hitting me in the arm and id flinch and pull it back off, bolts wouldnt tighten, etc. FINALLY got a good connection and the wipers and lights stayed on and wouldnt turn off (even if the key was out of the car). Tried to start it and just a sustained whirl or a spinning, almost like a vacuum cleaner. Any ideas? All help is appreciated!

First thing I'd do would be to check the battery cables for corrosion. Posts on here have shown corrosion up to 8" from the battery.