L700cx Memory problems

I have a Dimension L700cx PC, and recently the screen has been going black after 15 minutes use. Immediately after, the screen goes back to the desktop, but everything is frozen. This keeps happening until I shut the computer down manually. My sister was using the computer last week and did this, but now we cannot get it to work at all. There was a green light underneath the CD-ROM drive, and the fan was working (no power problems), but other than that, nothing worked. Neither the CD-ROM or diskette drives opened, and when I pushed the circular power button on front of the computer, it didn't turn on. The monitor did work, however. Also, the four lights on the back of the computer marked "A", "B", "C", and "D" were gray, when they were supposed to be green. The computer did not make any beeping noises. The ABCD lights apparently indicated a problem with the memory. I called Dell Customer Support in TX, and they told me that there was, indeed, a problem with the memory. They had me open the computer and "refit" it, and then try it in the other slot. Nothing worked. They then told me that they were going to send me another memory card, to replace the old one. Well, the memory card came today, and I tried every possible way to put the card into the slots without doing damage to the card, and still nothing works (same "signs/ symptoms"). The ABCD lights are still gray. Is it a memory problem? If so, why didn't the new card work? If it is not a memory problem, what is it? I would greatly appreciate any response that would aide in the fixing of my computer. Thanks.
-Amanda