I have a 2005 Quest that I have had loads of problems with (bad seal on driver door... brakes replaced and rotors resurfaced at 30k miles... new ecu... driver window won't roll up unless you hold the button the whole time), but now I have a very big problem.

I had the tired replaced a few weeks ago. Since then I've felt and sort of... drumbeat, I'd say, when I am accelerating from a stop or coming to a stop. The tire thing may be a coincidence though.
Now, a couple days ago, the brake light and battery light started flickering on and off sometimes. Always together. I figured it might be the cold (it's been very cold here lately).
Last night coming home I smelled a burning smell.
This morning I drove my son to school, and smelled the same smell. I stopped in front of his school, kept it in drive, then when he went in, I took my foot off the brake and.. nothing. I drove home at idle speed. Pressing the gas pedal did nothing, not even a sound. At one point it was like I hit a pothole, and the car started working again, and then I slowed down to take a turn, and back to nothing. The whole time the battery/brake lights were flickering, and getting dimmer, as if I was using up the battery.

Any thoughts?
I'm wondering if there are some belts loose? Sliding was the burning smell, and it's not letting the alternator charge the battery? Anything?

Thanks.