This thread shows what can be done with a Comcast. It cannot control presets. I don't know what groove is.
Some Radio Shack stores are running clearance sales on RS 15-100/133/134/135 remotes for $1 to $3. The have setup code 1658 which can control (with manual programming) presets.
Otherwise, the RCA RCRP05B, or OneForAll URC-8820N will work, but they'll be closer to $20.