I did this for a mate of mine a while back.
I used the following components:
* Creative 5.1 speakers with sub (Logitech Z680 or above is good, too)
* TV with at least two A/V inputs
* Soundcard capable of 5.1 (for budget, can't beat Creative Live 5.1 series)
* 2 x RCA male (standard A/V type cable) to 1 x 3.5mm stereo male (the standard plug at the end of headphones) adapter
* Graphics card capable of at least RCA output
* Plug DVD and Computer video output into TV, noting which A/V input is used. For best results, use SuperVideo plug, if available, rather than standard RCA
* Plug DVD output into computer audio input (digitally is the best, if you can)
(Personally, I would just ignore the DVD player, and use the computer's DVD playing capabilities. If you have an NVidia card, grab NVidia's hardware DVD decoding software, which kicks arse)
* Plug 5.1 speakers into computer
* Set up speakers around the room as per instructions (I've found that a towel underneath the sub can reduce reverberations if you place the sub inside a TV unit). You may have to extend the rear speaker cables, if so just use standard zip cable, and ensure you wrap the junctions in plenty of tape to avoid any wires touching another. If possible, use a soldering iron for this, otherwise, just twist the cables together as best you can, and wrap each wire in tape.
Above works well with a 2.1 high power computer speaker system as well. It is amazing how good they can sound in a small room or apartment. I use and recommend Creative 2.1 speakers. (And no, I don't have shares in Creative ;-) )
What else? Hmmm, grab yourself a wireless keyboard and mouse to complete the "armchair nerd" image.
And, for the REAL wow factor, grab a video projector. TV's are SO old school.... ;-)
If you just want DVD video with great sound, grab a DVD player that already has 5.1 outputs, and just plug the Creative or Logitech 5.1 speakers straight into the sound system with three of those adapters mentioned earlier. I also did this for a mate, and he was amazed. Total cost for setup was about $200 Australian!