I have the UT 2004 Demo.
Man it is a blast.
I have a 2ghz. cpu, 256 RAM (should get more, but am a cheapskate and it runs decently), with an Nvidia MX420-TV out video card, not one of the best and a bit old now, but it still plays UT 2004.
Will it play the upcoming Doom release? Not likely...probably would overload the card.
Both are not that much money. You could get an inexpensive ATI or Nvidia card that would be an upgrade. But the RAM would really be needed to play this game. That is, if the 2GHz CPU can handle it. This game is advanced so much so that even faster CPUs will choke when the action gets intense.