Bicycle Grip Shift

I have a shifter SRAM grip and yesterday my cable broke. (It's Indoor Cabler, not one attached to the derailleur. I removed the handle housing removed and the cable seems to be attached to the inside and there is no way that I see for the remove. I bought a new cable before removing the box, but there is no way, it seems to remove the old cable. Should I buy a new shifter with cable attached or is it a way to remove the old cable?

Here's how you do. You must pull on the cable inside the case.

http://bicycletutor.com/grip-shift-cable ...

Edit.
If you can pull the other cut the cable off the throttle or cut off the part that is frayed. Otherwise, you will need a new home.

http://bicycletutor.com/replace-cable-ho ...

On what end he break? If it broke at the end of the handle that you might have a problem. If so you may have to search the small end of the new cable into the output push to the end. You may have to turn the knob is the highest or lowest gear to get him out.
Usually, it is easy to change the cable. Thereshould be a screw which when removed, it is not like anything. This is where the old cable out and slide new cable in.
Do not forget the spin of the gear lever in each direction, but in general, would it turn the same way that you spin a motor to rotate the engine.
Hope this helps.