Champion Level 3Recording is good for initial setup of tests but you've just found out why it's not good in the long term. Those coordinates in your tests are never going to match any other machine and may not always match on the machine where they were recorded.
Take a look at name mapping here and see how to give those objects names and make your tests portable:
ETA: If you already have name mapping, then take a look at your setup. Did you also put TestComplete on the internal server? TC won't see the GUI across RDP. You can attach through RDP to run it, but TC must be on the same side as the application under test.
