The rest of the page above this is actually filled with alot of good stuff, and yeu might want to read up on them as well, even if they are lengthy. Some are not neccesarily ENTP-specific, but they can definately have influence in some ways.
The "I suck" black hole is much harder to be pulled out of though when yeu flat out ignore everyone's opinons to the contrary. An ENTP in that mindset will immediately dismiss anything that is considered 'good' or that they did 'right' by bringing up how 'that one doesn't count', or 'there was a flaw in that one' and so on. Positive reinforcement is virtually impossible to apply because they don't want to accept it. And considering the average capability of their debating level, yeu'll have to fight hard just to get the slightest glimmer of hope in there.
Every once in awhile though, someone may just blindly hit upon the perfect thing to crack the shell though. I've had rare instances where someone says one thing that just perfectly negates it. It's usually something that isn't even related, and just pointing something out that I had wanted to be appreciated on for some time, but had felt ignored on. However, this changes every single time so it's trying to hit a moving target, and isn't easy to do. And each time yeu miss, the target retracts further back, making it harder to hit. If yeu shoot blindly in the dark, they'll see it for whot it is and won't accept the right answer even IF yeu get it right after the 10th try. It'll be just dropped into one more reason why 'that one doesn't count'.
As I said earlier, and several others have subsequently pointed out... yeu aren't going to have much hope of helping directly. Yeu can't "fix" them in the way yeu'd like, and yeu can't even directly affect things once they get in this mindset. Any action taken only strengthens it. Yeur best hope is to let them cool off and indirectly aide that by ensuring nothing interrupts them. Any time as yeu so much as 'drop in to see how they're doing', it'll only make it take longer. Some people like the fact that people care about them in that manner, others, such as the entp, will take it as a frustration that they were interrupted in the middle of something. It's hard enough as it is for us to concentrate on a single thing at a time, and when we do, it's a very relaxing feeling... until something interrupts it. Then it's just irritating to the core.