You don't mention what you have configured on your TMG but this is basically how you do it:
Before doing anything, backup the server and export the TMG configuration. Do this while physically logged on to the server.
Change the external IP first.
- change IP address on ext nic through Getting Started Wizard, apply the settings
- change any server publishing rules and web listeners that are using a specified IP address
When done and all is verified to be working, move on to the internal ip address.
- Change the IP address from within the Gestting Started Wizard. Apply the settings
- validate all network objects and update the ones that need to be updated with a correct IP address. Don't forget to look at the system policy as well.
You may need to alter the SQL configuration as well:
SQL Server Configuration Manager / SQL Server Network Configuration / Protocols for MSFW/ISARS / TCP/IP / IP Addresses (most likely only ISARS)