QTP 10 can connect to QC 9.x, but QTP 9.x cannot connect to QC 10, thats all.
try to open your QTP test from QualityCenter
1.) open QC
2.) login into your project
3.) select the test you want to edit
4.) select the script preview in QC (only available with QTP AddIn for QC)
5.) press the button "Open with Quicktest" in the upper left corner of the tab window
The QTP add-in to QC is not related to the connection. the add-in is enables you to see QTP test type in QC, execute QTP tests and see the test script (and keyword view) in QC.
Without the add-in you should still be able to connect from QTP to QC
As asked before - what are the QTP and QC versions that you are using
I think the Addin in not installed properly.Please try to reinstall the Add in. Please make sure that you are selecting the correct version/ compatable version of Add in from the list of addin available in QC.