I hope you purchased the right part, Apple in their infinite wisdom made the connectors slightly different from 3G to 3GS. It could also be that you bought a faulty part, the failure rate from eBay is quite high because the parts are usually factory seconds,
It could simply be the battery is below the charging threshold. If you feel confident you can dismantle it and have a multimeter, dismantle it and test the battery. if the battery tests as less than 3.7V then follow the instructions here: Think I've been sold a dead iPhone 3G... - Logic Boards?
It's most likely the phone is beyond repair by now. Salt water is incredibly corrosive and if enough got in to short circuit the battery, some damage has occured. Salt water damage can SOMETIMES be fixed but rarely after letting it sit and corrode for two weeks. You might as well pull it apart and have a look.
It sounds like you only need to replace the digitiser. This is stuck to the LCD and requires some skill to seperate and stick the new one on. Be sure to wear eye protection when removing the cracked one. Here's the instructions : iPhone 3G Front Panel Replacement
It's not ideal and is unlikely to work long term but try some squishy foam, like earplug foam and perhaps Blu-Tack if you jam it in the phone then close it, it MIGHT provide enough pressure to work. If not, you're up for another LCD. Or if the damage is to the Logic board you're in real trouble.
It sounds like the battery is below the charging threshold. A LIon battery needs to be around 3.7V for the charger to kick in. We usually dismantle the phone and connect the battery directly to a 4.2V source with multimeter attached to see when it reaches 3.7V, usually it takes only a few mins to get to 3.7V. Once this is done, you can connect the USB cable and charge normally.
The biggest problem with dismantling it yourself is you will void the warrantee. You MIGHT be best taking it to a Motorola Service Centre and getting them to do it for you. IT will likely cost $20-$40. However the cost pales by comparison to the risk of damage and losing your warrantee on such an expensive phone.