I by far am not an apple guru. Honestly I have never taken apart a 3gs iPhone nor installed a digitizer on one. However I have installed a great number of digitizers on other items.
You could try to reset the iphone (press the sleep and the home button at the same time until the phone restarts). Never know, it may come around. If that doesn't work do check your connections. Inspect both the male and female parts to the connections for debris, bent or broken pieces. Make sure that all the pins are lining up properly. If you still have your old digitizer compare the connector on it to the one installed now. You may have been shipped a 3g instead of a 3gs digitizer. I believe that the 3g has more pins than the 3gs digitizer. If none of these help you then contact the place where you purchased it for an RMA.