Unfortunately I'm not sure which DVR model, it's whatever TWC provides - two years old.
I think the remote is likely the default basic one, it's pretty rudimentary - the top third is made up of function buttons like play, forward, rewind, etc; the middle section is guide, menu, info and a circular pad with up/down buttons; the bottom third is 0-9 and a last button.
Make sure the Slingbox is configured for the correct Time Warner cable DVR. You will want to make sure you find out the exact model. If you do not know what it is, it is printed on the front face of the cable box or on the back label. Below I will provide a few articles to get you started. One will show you how to configure the Slingbox input for a new remote, and the other will allow you to search for a specific model video source or by provider.
- I got a new cable or satellite set-top box and now I can't control my TV
- Help finding your video source with the Supported Video Sources Tool
Hope this helps!
Sling Media Moderation Team