Can I use Bind Monster in addition to the combat check?
If you fail to cast a spell, none of its effects happen. So you're left exactly where you started: you have a combat check to make. Of course, Bind Monster is two-handed, so... you won't have any weapons and may not fare too well in the check.

(Side note: combat checks are a special kind of fight check; this is a combat check, not just a fight check.)