The touch screen is made in layers. It is possible to crack it and the touch still work. It is also possible to crack it a bit more and the touch won't work. What's more, once the first layer is broken the remaining layers are far more vulnerable to breakage.
At any rate. Your only option is to get the screen replaced. The good news is the iPad 1 is far easier to fix than the iPad 2. Since you are probably no longer covered by warrantee there are third party companies that will replace the screen, so you can shop a bit to see if you can get a better price than what Apple will charge.
Make sure you take a good hard look at the company though. You often get what you pay for, and super cheap usually means corners cut, or shady business practices. If you can afford it, Apple is the safest bet.