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.