'05 Grand Am Starting Problem?

Well, its my first car. 47K miles, bought it used. Was a good car the first month or so, but then it had troubles with starting. My auto-mechanics teacher thinks its my fuel pump, but lets see what you guys think.

Heres the situation. The car sometimes starts perfectly fine, turn the key to start, right on perfectly. Other times, I turn it to start, and it goes for a few seconds and never turns over. And all the lights go out in the car(gauges and stuff), and it just seems really week. Other times, I turn it to start, and its not turning over, so I go back to on, and it continues to try to start, sometimes even 2-4 seconds after its been switched back to "on"!

Now, my teacher gave me advice to switch the car to "on", for about 10 seconds or so, then start it, and see if it helps, that way you see if the fuel pump is getting pressure. Well, I guess it seems to start somewhat better, but it still doesnt start normal sometimes. Also, a few times, I have started it, and it never turns over, then it seems to die for a half second, then it makes a screeching noise, then it continues to try to start, then finally does.

Please, let me know what my problem is and how much it would cost to repair at a shop. Thanks!!