Being AN administrator is not good enough under UAC, you need to be THE administrator.
To install QCClient (QCExplorer):
Either turn it off as SergLA has suggessted or right-click the installer and choose "Run as administrator", then allow when the UAC prompt pops up and you should be fine.
To use IE7:
The *first time* you connect to QC with IE you need to launch IE "as Administrator", this requires you to right-click on the quick-launch icon and choose "Run as administrator"
Once all components have been downloaded/installed you can launch IE as normal.