I know the feeling
I bought a Alienware Aurora R4 the first part of Oct 2012.
When trying to boot for the 1st time, all I got as 1 beep and a blank screen. Called Alienware support and they had a tech out the next day. Took him 5 minutes to find out the computer was configured with the wrong OS at the factory. Where is the quality control?
Things went OK for about 6 weeks then I started hearning a clicking noise and the graphics were terrible when playing games. Called support again and two days later a tech showed up with a refurb Nvidia 560ti graphics card which was a low end OEM card with lower specs.
Now I hear a high pitch noise that comes and goes and is very irritating. Taking off the side cover I can trace it down to an area of 4 fans, but can't pin point the exact one, So will just have to wait until something dies to figure it out.
The only cure would be to have a tech come out with every fan, change them one at a time until the noise is gone, that is not going to happen.
I have not had near the trouble you have had and the tech and sales people at Alienware have been great to me, but these are not $399.99 computers pulled off the shelves at Staples or Office depot. For the money we pay for these computers I expect a lot more than we are getting, but Dell sees it differently and a $300 computer or a $3000 is all the same to them.
I bought a 3 year, next business day warranty with mine and glad I did. Looks like I will be using it alot.