I just picked up the car on thursday, and right after getting it home it wouldn't start. I went inside for a while to calm down a bit, and when I came back out it started fine. I put about a hundred miles on it since then.

When I tried to start it this morning, the same thing happened. Turn the key, and nothing. No sounds whatsoever. I left in my other car since I had someplace I needed to be, and when I got back the problem hadn't resolved itself like it did before. I tried to jump it, but that had no effect.

If this were my other car, I would check the points, coil, and starter solenoid first but with the bonneville I have no clue where to begin. This is my first time working on a modern engine, so any suggestions would be greatly appreciated.

Ok, lets start with the basics first.

Check your battery cables for corrosion. Top and bottom.

When the car won't start, do your power windows and locks work?

When you turn the key on, (not start) do you hear the fuel pump?

As the car does nothing when you try to start it, you may have a VATS issue. What does the security light do while your trying to start it? Try cleaning the little pellet on the key with an eraser, and put some alcohol on a Q-tip and clean out the ignition switch...see if that helps. And/or try a second key if you have one. This along with what Mike said, as corrosion is often a problem.

I already cleaned the contacts with a wire brush and replaced the battery. Tthe power windows, locks, all the lights, and the radio work just fine. I do hear the fuel pump, and after trying to start it a few times I can definitely smell gas, so that most likely isn't the issue.

The security light stays on for a few seconds while I turn the key, but then it goes off.

Edit: I don't know if this is normal, since I just got the car, but if I hold the key the check engine and check gauges lights stay on when the rest go off. Also the oil pressure gauge stays at the far left, even though the oil is full. Could this problem be caused by a faulty oil pressure sending unit?

Is this while the engine is running or off?

off

Well, if the engine is off, the oil pressure gauge is going to be at the far left position.

When you first turn power on, the system does a self check. If you haven't started the engine yet, your check engine light and check gauges light is going to stay on. Your ABS will go out if no errors are found. After sucessful start, the check engine light should go out along with your check gauges light. Unless you are low on fuel or your washer reservoir is empty.

It seems like its most likely a starter issue then. I'll have to take a better look tomorrow.