First, your not running the "Splinter Cell Mod", there is no such thing.
Splinter Cell is the game you used to load the exploit.
You are running Krazie's, Kingroach's, PBL, etc...
If you are running Krazie's Ndure, you should be able to load the game from the original CD and play the game on Live. That is, if you meet the marriage theory.
If you Xbox was on Live before the mod and you have the original HD, you are OK to play on Live.
If you were on Live before the mod and have upgraded your HD, you need a new eeprom that hasn't been on Live before.
When the Xbox is booting with a DVD in the drive, it bypasses the softmod.
When you boot without a game in, the softmod hijacks the Xbox and runs the BIOS (softmod) you put on there through the exploit.