I just had this happen to me.
At first, after replacing the cracked cover/digitizer, the LCD was working but digitizer was not. It was late so I went to bed and left the ipad on my desk for a day or two. When I came back the LCD wasn't working. I charged the ipad and pressed the power button and still nothing.
Here is what I did:
1) Wimpered a bit.
2) Used air to blow out the connectors for the digitizer and LCD.
3) Used an LCD cloth to clean the ribbon cables, just the connector portion, making sure to rub towards the end that plugs into the connector...as not to damage the small copper connectors.
5) Inserted the digitizer ribbon cable into the connectors and used the plastic glass removal tool that came with the digitizer to carefully but firmly press the ribbon into the connector.
Tricky part. The digitizer I bought had lines demonstrating the depth to be inserted into the connector. I had to press the cable in until I couldn't see the lines anymore before the digitizer worked. Kinda nerve racking to be semi-forceful with delicate components. But I'm used to it since my girlfriend is 5'0. I digress...
6) Without completely reassembling the ipad I put the LCD into its compartment and the digitizer over the LCD just enough to have functionality of the omnipotent front button.
7) I pressed both the power button and front button at the same time and held them down for 15 seconds and voila!! Everything was back to normal.
I'm actually writing this on my ipad no more than 30 minutes after this repair. :)