Prius (Gen 2) :: Battery Replaced, Car Is Going Harder / Heater Varies Heat

I bought my 2006 Prius a little over a year ago from a Toyota dealer in the area, and within the first month I had a strange occurrence. I got into my car, pressed the power button to start the car and everything on the dashboard lit up, the power button flashed amber, the clock's numbers were just barely visible, and the car wouldn't start. Frantic that no matter what I did (shut it off, took the keys out, and tried again several times with the same results), I called the dealer who sold me the car and just as he was about to send out a tow truck to get me, I tried it one last time and it started. I took it directly to the dealership, they inspected it, and came back with the response of 'there's nothing wrong with it, I don't know why it did that. If it happens again, come back again.' No charge and supposedly no problem, I let it go.

Well, exactly 1 year later (to the day) and suddenly it happens again. So I take it to the dealer again. They checked the battery in the back and now they're telling me it's a bad battery cell. They insist the two incidents are completely unrelated. I left to go to class that night and had no more issues that day. But now I have a car that's been getting harder and harder to start. The power button doesn't even light up green anymore. I've noticed that I have issues when I open my door and the alarm goes off like I've left the key in the ignition, but I haven't. I knew when I opened the door yesterday and the alarm sounded that I was going to have issues. Sure enough, the car wouldn't turn on, and after two tries, it became completely unresponsive.

Which battery has the bad cell? They tested in the back, where the hybrid battery is. Also, it seems like there's something more serious than just the battery, considering I've read the manual a zillion and one times since I first had issues in hopes of trying to figure out what's been going on. The power button, like I said, flashes amber when it turns on, then disappears once it's on, but there is no green light instead.

Also, I've been getting repeatedly worse and worse gas mileage since the fall, the last fill only lasting me 350 miles or so with an mpg average of 34.6. I know it's winter and that the Prius typically gets worse gas mileage in the winter due to the heater being on. But the funny thing is, I don't drive with the heater on, even through the winter. I only use the heater when I need to defrost a window or I have company in my car because I like the cold. However, I got stuck on the I-90 for about 9 hours in the beginning of December and I noticed then that the heaters for the feet was varying how much air was blowing out of them after a few hours, and ever since then it's had the same problem. I figured it might have been a need to change the cabin air filters, but now I'm wondering if it points to something else...