puzzling problem with my cavalier

I have an 02 Cavalier. My problem is this: a few times after starting the car my battery light, engine light, and oil light all come on and the brake locks so I can't press in down to shift out of park. The last time this happened I shut the car off and on with the same thing happening a few times then it just wouldn't turn over. The radio wouldn't even come on. I replaced the battery and it started right up. But the battery was just replace a little over a month ago after my car wouldn't start one day. When the whole ordeal happened before a few times I'd turn the car off and back on and the lights would be off and I could shift out of park. I know a few mechanics in the family and nobody has a clue why it would do all that. Any ideas? I've been thinking its the alternator but that to me doesn't explain the brake not being able to be pushed down or the extra warning light on.

with everything that is coming on, I think that the ignition switch needs to be replaced`

i would do a voltage drop on your grounds going from your battery to engine, then to the body as well.