In case you aren't aware of its existence, you might be interested in XBMC. It's a mature (just celebrated its 10th birthday), popular media center app which can be installed on Ubuntu (and other unix-like systems).
You asked if your old server is too slow but neglected to provide any tech specs. I have never used XBMC myself, so even if you provide more info I cannot answer that question. A possibly quick way to find out for yourself is to download their live cd,
XBMCbuntu. If the live CD works well, you can choose to install XBMCbuntu from the LiveCD or to install the XBMC package after installing Ubuntu.
Here's a short demo to give you an idea of what to expect from XBMC and a link to an article referenced by the video description:
Youtube: XBMC Media Cener Demonstration
Lifehacker: Create a Kickass, Seamless, Play-Everything Media Center: The Complete Guide
Regards,
Alister