My Display Only Works Part of the Time and Apple Care Won't Help Me (Long)

Question

I bought my computer at a discounted price because it was a restocked item, but was it really worth it? I'm beginning to think not. I saw that it had one stuck pixel, but saving that much money on such an expensive computer, the pixel hardly seemed like a travesty. However, I think I've discovered the real reason why the last owner gave up such a seemingly exceptional piece of hardware...
After about a month of flawless operation my "new" computer started to act a little strangely. It wouldn't always go to sleep when it was scheduled, the screen saver wouldn't always come on by itself...things that I though a simple PRAM reset, SMC reset, or disk permission repair would fix. After countless attempts at all three "fixes" I was still having problems...a few days after these problems started occuring something even more drastic happened: My computer would turn on (the little light would come on, I'd hear the fans start running and the start up tone) but the screen would remain black. I tried several PRAM and SMC resets as suggested on this forum, but the screen continued to come up black for about an hour. That's when I called Apple.
The Apple Care specialist on the phone asked me for the serial in which I had to lift the computer up to get (since I obviously couldn't read it off the screen). She suggested an SMC reset which, I explained to her, I had tried already but it hadn't worked, however, I was willing to give it another shot. Oddly (and rather annoyingly) enough it worked, and for a short amount of time I was happy...until it happened again...another call to Apple...and again...and about 3 or 4 calls to Apple Care later, they suggested that I go in to an Apple Store to have it looked at.
The Apple Specialist made an appointment with me to meet with an Apple Genius the next day at 4:30PM at a store about a mile away from my house. The next day I lugged my 24" iMac through the local mall (I'm female, 5'2", and I weigh about 108 so it wasn't too easy of a feat) to discover the apple store was CLOSED for the next few days so that they could "make the store better." I called Apple Care on my cell phone right there in the mall and asked them what was going on. Didn't they know that this Apple Store was closed? The man I was talking to said that they knew and he wasn't sure how the person I had talked to just the day before had signed me up for an appointment when he hadn't even asked for my e-mail address. It was most bizarre. This man made an appointment with me for later that same day at an Apple Store about 45 minutes away from where I live. I didn't want to go, but I'm a college student and I was a desperate for my computer to work again.
Shaking around in that box must have brought it out of it's strange seized-up state because as I brought it out for the Mac Genius to look at it turned on for him no problem. Quite a frustrating problem because it's so spontainious that it keeps making me look like either a liar or a fool. He said he'd run an 8-hour diagnostic check on it and I could pick it up the next day. So the next day I waited for their call but I got none. I called them and they said that they were still running tests and it'd be ready the next day. The day after, about an hour and a half before I had to go to work, they called me and told me my computer was ready. They said they had ran a 24-hour diagnostic and everything was working fine but they said they'd run more tests if I wanted them to. I'm a full-time college student and I need my computer for just about all of my classes, so I declined more tests and told them I'd pick it up right away. I dashed over there to pick it up and dashed back as fast as I could (and I even made it to work on time...but just barely). Later that night I found that they had accidentally left their diagnostics CD in my computer (I called them about it and they said that would like it if I would bring it back...I still haven't mailed it).
All was fine and good (well, just okay...it still had problems with its sleeping and screen-savering) with my computer until yesterday. I got that black screen again upon start up....but this time my "fixes" worked after a few tries. There were no more problems for the rest of yesterday.
However, today I came home from school and go to start up my computer and the screen turned on and I saw the little mac symbol and that little circle of bars...but then it froze. I held in the little button to force a shutdown and when I started it back up again I was greeted by my good old friend, Mr. Black Screen. Just wonderful. I tried my "fixes" but today I didn't get lucky. So while I was holding in the button to start up my computer (again) and give it another go, I held it longer than I was supposed to and the little on light began flickering. Then I heard this unpleasant tone that lasted a few seconds before stopping and treating me to the startup sound. This time the screen turned on. Yay! I go to call Apple to find out what I had just done, and I find out that my 90 days are up and unless I wanted to pay $50 for them to be puzzled by my issue once more or give them $300 for not quite 3 more years of service, I'd have to lug my computer to an Apple Store or post here to get help. Thanks a lot Apple Care.
My "new" computer cost me almost $3,000. It should work the way it's supposed to. I need it to last me no less than 6 more years, but with the problems I've had with it in the first 3 months (which seem only to be getting worse and more frequent), I don't know if I'm expecting WAY too much out of it. I've been a loyal Apple user for 13 years and out of the 5 computers I've had in that time I've never had so many problems (actually I've never had any problems, at least nothing really serious; I'd never even called Apple Care before this). I'm a fairly experienced user (I'm not a Mac Genius or anything, but I know the ropes) and I am sure this is not normal behavior for an Apple computer (or any computer of that matter).
I'm so frusterated I'm not sure what to do. What's wrong with my computer? How can I get Apple to help me? How can I get Apple to even believe me? Any advice would be greatly appreciated and thank you so much for reading my very long (and rather dramatic) story.

Answer 1

Thanks for reading and thanks for the advice. Perhaps I'll ask them about it next time this problem occurs, although carrying the thing through a mall that is only about a mile away is the least of my worries. I'll do if it is both free (I don't make enough at my job to pay for such a service) and relatively speedy, although I'd hate for them to come over and for the computer to work properly (as bad as that sounds). It'd be a wasted trip and nothing would get fixed.
I'm contemplating videotaping myself performing my "fixes" on it the next time I have this problem.