How do you get tech support to respond?

In my experience, the short answer is: try, try again. After the internal CD-ROM drive failed in the Latitude C800 I have, the company tried to warranty it. Because there was classified information on the hard disk drive, the drive was removed before sending it in for service. Dell refused to service the laptop. I ended up buying the laptop from the company and transferring the remainder of the warranty term (a year and a half on its three-year all-options warranty) to me. I then spent the next year plus trying to get an RMA issued; this involved hours and hours of staying on hold, being disconnected, and bounced from department to department. No one would issue an RMA number. No one would even sell me a replacement CD-ROM. The month after the warranty expired, I called Dell again, and a cheerful woman offered to sell me a replacement CD-ROM for about $100.00, or a DVD-ROM/CD-RW combo drive for about $200.00. I looked on eBay and bought a CD-ROM drive which works, though the tray bezel doesn't line up, for $10.00 ($15 after shipping).
I have worked as a computer technician for most of the past seven years, 80% of it on Dell hardware; many years, I have performed upgrades or (much more rarely) repairs on a thousand or more Optiplex computers alone. In my experience, Dell make computer hardware that usually works well, and as long as you take care to buy Dell-certified parts, you can expect repairs and upgrades to proceed smoothly. In my personal and professional experience, trying to get Dell to fulfill their warranty contracts is an utter waste of time. If you still can, return your laptop to them and then turn around and buy another. In my experience, Dell's failure / defect rate is actually much lower than other manufacturers.
You don't specify what behaviors your Inspiron is exhibiting. Doing so, taking particular care to correctly identify in sequence the events which are occuring and the circumstances in which they occur, would be most helpful in diagnosing whether the problem(s) is(are) hardware based and if so whether it is the laptop or an accessorie, or a result of the operating system, or of a non-operating system program. I.E., if the problem is that your USB mouse displays erratic behavior, it would be good to know. Dell support's answer to everything seems to be "reformat the hard disk and re-install your software"; unfortunately, I've ended up talking personally with Dell department vice-presidents on three separate occassions on three separate issues (most recently, about six months ago), and have never received an answer on any of the issues discussed.

Honestly, it sounds to me like there's some piece of software that you're installing that's having an issue. Have you run virus and spyware scans? There are multiple thousands of spyware apps that will cause similar problems to that which you describe.

What apps do you load on your system? One of them could be misbehaving. It really doesn't sound like a hardware issue if reformatting the drive fixes it. Being a software issue, is it really even up to tech support to fix? Besides, their fix (nuke and pave) seems to work, even if it is a royal pain in the rear. Perhaps we can help you out rather than you having to go through tech support.

I doubt that it is a software issue because I have been having problems from the moment that I reinstalled Windows and before I installed any other programs. This goes for both after I reformatted and after Dell had me install a new hard drive. With the new hard drive they also supplied me with cds that contained Windows and all the drivers I needed.

When does your laptop "freeze up for a few minutes"? Which is to say, describe in as precise detail as possible; you may find it helpful to select this text, copy & paste it into your response box and then fill in the blanks:

1) where the laptop physically is [on your lap; on a table (with/without books either side, allowing good air flow); on a specifically-designed laptop stand]?

2) what Operating System are you using? (Red Hat Linux, Gentoo Linux, Windows XP Home, Windows XP Professional, Windows Vista (version))?

3) How much RAM do you have installed?

4) A) What programs do you normally have open? Be sure to give version, for example, Internet Explorer 7.

B) What many windows (For example: 3 Web pages, 1 e-mail program window, 1 instant messanger with 2 open chats.) do you normally have open?

5) A) What program window is most frequently on top when your laptop ceases to respond to you?

B) What programs are running in the background when your laptop ceases to respond to you?

6) Keep Task Manager open.
A) How much physical RAM does it show available?
B) What percentage of CPU useage is shown when the computer is:
1) in normal use?
2) frozen?
3) immediately after the laptop begins to respond, after freezing up?
By keeping Task Manager open, running in the background, you will have a histogram (a chart of activity over time) from which you can get the answers to this question.

7) A) What anti-virus software are you using? How frequently do you scan (full scan, heuristic sensitivity high)?

B) What anti-spyware software are you using? How frequently do you scan and how deeply?

C) What firewall software are you using? Have you specifically enabled all ports, servers, and services necessary to your useage, and dissabled all others?

D) What form of internet connection(s) are you using, and where (dorm, house, apartment, work), and is the connection shared? (An unstable WiFi connection will frequently cause problems to apparently unrelated programs, as resources are diverted to reconnecting.)

E) When the laptop locks up, are you on a chat site or an online game? (This question is asked specifically because "script kiddies" are notorious for picking their marks during online activities such as these. No offense need have been given; as often as not, they're simply trying out some softs/scripts/warez they've downloaded.)

8) A) 1) Do you use a hard disk utility (SeaTools, for example) to perform a full confirmation that your RAM, Motherboard, drive controller(s), and hard disk are functioning optimally, and perform a full zero-write to disk before formatting and installing your operating system? 2) Have you used a program such as memtest86 to specifically test your RAM for errors?
B) How frequently do you perform a full Disk Check and Disk Defragmentation?
C) Do you always perform a "graceful shutdown", by using Start->Shutdown->Shutdown/Restart (Windows key->u->u for short), and waiting for Windows to cycle off on its own, even if it seems to take a while? How long does your operating system take to shutdown, from the time you click on "Shutdown"? (Don't guess! Time it with your watch!)

This may seem like a lot of questions to answer, but I assure you every one of them is not only valid, but essential given that none of us are there to physically look over your shoulder to witness the computer's behavior first-hand.