Charleston PD radio traffic is carried on the Palmetto P25 system. Dispatch talkgroups are 2010 for Penninsula and 2011 for West Ashley. This is the same system that all Charleston County agencies use - Charleston Co FDs, SD, P&R etc.
Here's the RR database page that contains all the information you need:
Palmetto (P25) Trunking System, Various, South Carolina - Scanner Frequencies
It's worth noting that there are several transmitter sites in Charleston for the Palmetto P25 system. Make sure you program site #1 the Charleston Simulcast site. It's the one that will absolutely carry the traffic you're interested in hearing.
It's also worth noting that this is a P25 simulcast system which is very difficult for consumer-grade scanners to monitor. It's a well documented problem. You may not be hearing much from your location because of this issue.
Simulcast digital distortion - The RadioReference Wiki
You will have to either send your radio back to whoever programmed it originally with this information or learn how to program scanner yourself and verify if the information is programmed properly and completely. If not, you'll have to add to or modify the original programming.