remote issue and trunk opening on it's own

I have a couple of things I need some help with. Any feedback would be greatly appreciated.

I bought a 1998 Oldsmobile Intrigue. The keyless entry remote doesn't work. I bought a new battery, but that didn't remedy the situation. I was told I could go on E-Bay and possible find a replacement there fairly cheap. My question is this, how do I program another remote to operate this particular vehicle? Is it something I could do myself, or would I have to take it to an Oldsmobile dealer and let them program it?

NEXT!!!

The push button inside the car that opens the trunk is missing. You can reach inside the space and push a little button. It will make a clicking sound, but the trunk will not open. The weird thing is while you are driving down the road, and hit a few bumps, and then when you stop and check the trunk, it will be partially open. It will not fly up or anything, but you have to close it back. The electrical connection was unplugged when I bought the car today. I plugged it back up, thinking it might make the trunk release when I pushed the little button inside, but it did not. Is it possible that the electrical connection could be causing the trunk to release, after hitting a bump in the road? Just asking, cause I've never had a trunk to come open while going down the road.

Thanks in advance.

 

There are many sites on the web that offer reprogramming instructions for a price. Might even still be a few free ones. Since each year, make, and model seem to be different, there are no generic instructions.

The trunk problem, along with the missing button, sounds like an intermittent short. I would track the wiring from the dash back to the trunk, carefully looking for pinch points and worn / cut insulation. Also check the button you refer to.