It will be very difficult to completely dry out the carpet because of the sound deadening material. Ideally, you will need to remove your seats and carpet and sound proofing, which will probably be a sodden stinking mess. You can either dry it out in your garage or renew it. The carpet, once it is out, will dry fairly quickly.
When the carpet is out, you can then check the floor and the bulkhead for integrity of the sealing.

Bugger you Ben. You hit the post button before I did!
