I want to make a DVR box  out of a computer that I already have. I
know there are many programs that allow you to do this, however, I
have several limitations that I would like to be resolved.
First, I have a subscription to digital cable, so I would like the box
to be compliable with it in a metter that it can record programs
without me having to be at the tv switching the channels.
Second, I want to be able to play back recorded TV from the box using
a remote, I do not want to have to sit at the computer because I am
trying to make it so the computer is only hooked up to my TV, no
moniter.
Basically, I want to be able to use my PC as a standalone TIVO, with
almost unnoticable video quality difference on a 32" TV, while being
able to record video to dvd, control the DVR recording via remote and
use the computer to play music and such.
I am trying to do this project for under $300, and without having to
pay any monthly fee. I already have a computer with a fairly quick
processor, the things I am planning on buying are the tv card, a
bigger hard drive, software (linux if needed) and a remote system.

Sounds like what you want is either windows media center, which will
end up eating a large chunk of your budget, or MythTV
http://www.mythtv.org which is a free linux based DVR software.  For a
remote control, since MythTV does not have native remote control
receiver and decoder software built-in, you'll need to install lirc,
which MythTV can cooperate with.  lirc stands for Linux Infrared
Remote Control program. lirc handles the IR hardware and passes
keystrokes to MythTV, which then acts as if you had pressed the keys
on the keyboard.

This page lists the hardware requirements for MythTV:
http://www.mythtv.org/docs/mythtv-HOWTO-3.html#ss3.1

There is also a MythTV livecd called KnoppMyth which makes the install
of MythTV pretty easy.  http://www.mysettopbox.tv/knoppmyth.html  and
http://knoppmythwiki.org/ are the web pages you want to look at to get
details on that.

Oh and I almost forgot, to control the digital cable, you have a
couple options, one hope your box is compatible with firewire and can
be controlled directly by MythTV.  Alternatively you get a serial
irblaster, and control it that way.

Lifehacker.com has just posted a story on this exact topic.
This link shoul get you there:
http://www.lifehacker.com/software/dvr/hack-attack-build-your-own-dvr-165963.php

I think that Freevo (http://freevo.sourceforge.net) is the sollution for you.
Freevo is an open-source home theatre PC platform based on Linux and a
number of open-source audio/video tools. MPlayer and/or Xine can be
used to play audio and video files in most popular formats. Freevo can
be used both for a standalone PVR computer with a TV+remote, as well
as on a regular desktop computer using the monitor and keyboard.