Most universal remotes don't have remote codes for the off-off brand Advent. Just as well, it's not a particularly good HDTV, but it was cheap and better than my old tv, plus it's HDTV ready (though I still need a converter; haven't actually seen any HDTV on it...). I have the Advent HT 3061A.
Recently, I got a One For All universal remote URC 9910, which didn't list the tv. A web search was no help. So I called the company, 330-405-8616. They were very helpful. In order to use the remote (which just arrived this week) on a tv (which I got about a year ago), I needed to upgrade the remote. The company very kindly e-mailed me a sound file (since the quality over Skype was insufficient).
To upgrade your universal remote for this model of Advent, you will need to play this soundfile into your remote, then use the tv remote code of 0842. Call the company and play the sound over the phone, or have them e-mail you the file. I don't see a microphone or any sound input, but it works. Added: Just called again, and it turns out that the remote has a modem inside. Presumably just the dem part, since it has no output, and they couldn't tell me what baud rate, but that's still rather neat. The USB connection, mentioned in the replies, would still be a better interface, but you take what you have.
I'm still playing with the remote, which is enormously complicated to set up. I didn't expect it to be this complicated, and shouldn't be. The remote comes with enough buttons that I shouldn't have to manually assign this many keys. I've never been happy with any universal remote, and never buy them. The only two I've ever had have been free, including this one (a prize for three years of Harris Poll participation). Still, the One For All has a nifty feature that I hope to enable: The remote itself is both IR and RF, and comes with an RF station that can sense the remote from outside line-of-sight and then beam an IR signal to the components. So far, that works, saving me a bunch of stretching.