Another 12v battery problem (02 prius)

Hello,

I just spend around half an hour typing a post detailing my problem and all the specifics + details but then priuschat logged me out when I tried to post it and so I lost it all.

Long story short: '02 prius, someone left a light on, won't turn on, AAA jumps it and I get error screen with third error highlighted, decided to replace with Miata batt from elearnaid, installed battery.

Now here I'll elaborate a little, after I installed the battery, the car appeared fine with lights on and all that jazz, turned it on and seemed fine. I didn't have to go anywhere so I just turned it off after that. A few days later I tried it and it acted like it did when AAA jumped it - the error screen still shows up, the check engine light turns on (may be a new development for all I know), and the car moves SUPER slow because the gas engine cuts out after a few seconds.

SOMETIMES (very rarely, occasionally only after many successive attempts) when I turn it on, I get no error screen/check engine but the car still moves really slowly and I don't want to take it out of the garage. This usually happens after I fiddle with the new battery. When this happens, on the engine monitor screen, the battery's charge is usually listed as very low - around 1/4th or 1/5th full. I followed the instructions very closely because I was afraid that I'd die if I didn't so I don't think the installation's the problem, although the connectors that came with the kit don't go all the way down on the battery terminals - they probably only go on about halfway down. Other than that, all connections are TIGHT.

If anyone's had a similar problem or just has some advice please let me know. I'm a working student right now and don't have too much free time in the first place, but this new problem is now eating up all of it . Sorry if this post is a bit uninformative or anything but I lost a lot of information from my first post and I'm too frustrated to go typing it all again. Thanks in advance.