Problems with my 2008 Prius

Day started out fine until all the warning lights came on all at once. Never had a problem with this car before. I was so far from home that I started to look up some of the warning light descriptions and decided that it was probably the battery and I might be able to make it home. The only problem I could detect was that I lost my cruise control and my A/C. Other than that the car was driving fine and there was no noise. Then the brake light started to come on, and then buzzer went off, this would happen about every 40 miles. Then the car started to shift into neutral and I was losing power. I was able to shift back into drive but even that ability was soon gone. I was 7 hours from home and left with no choice but to find a hotel fast and spend the night until someone could come get me and tow the car home.
So my question is this.......is this the fault of my 12V battery going bad? When I looked at my display, I still had a lot of blue bars. I have read where Toyota says it is impossible for the car to shift into neutral, but it can and it did! I was also losing my brakes.

 

Has 81,000 miles on original battery. Would this have caused all the problems I was having....with the car shifting into neutral?
And where would be the best place to purchase the battery. I'm a DYI type of person and have handle most of the minor repairs to the car myself. I checked on Amazon and they have the battery for about $150.00. I've checked out u-tube videos and I'm pretty confident that I can handle the replacement.

What will that tell me?