The Pro HD's tuner can handle NTSC, ATSC and QAM (unencrypted digital). It'll definitely handle whatever your Sling Tuner is hooked up to.
If you come across a Sling Pro or Classic, they'll work with the same kind of analog cable service as the Sling Tuner.
If you wish, Sling will repair/replace an out-of-warranty Slingbox for a set fee. I think it's $100 for your model. Here's a link to information on that:
I think you're better off picking up a different model Slingbox instead of having them fix your Sling Tuner though. You'll end up with a lot more capability out of the deal... the Sling Tuner is the most limited of all models.
Hope this helps,