Hi Homerj,
QC 10 and prior versions had a different back end coding and sometimes this caused the patches to not eb uninstalled when the main application was uninstalled.

I would recommend that you uninstall any patches that may remain, reboot, and then if the issue still persists try the following steps:

Choose Control Panel > Add/Remove Programs, select, and click the Change/Remove button. Follow the instructions on your screen.Locate the ALM Platform home directory ([drive]:HPALM-Platform). In the _uninst subdirectory, double-click uninstall.exe.

If that doesn't resolve the issue then try the following:

If we want to install QC ALM you need to remove the previous version(s) ALM 11 / QC 10 / QC 9.x.
To verify that ALM Platform is not installed:
1 From the Start menu, choose Control Panel > Add/Remove Programs.
2 In the program list, check for HP Quality Center (QC 10 or 9.2) or HP Application Lifecycle Management Platform.
3 If either appears in the program list, click Remove, and follow the instructions on your screen.
4. Renamed the vpd.properties file, found under C:Windows & moved to other place.
5. Restart the Server.
6. Now, try the ALM 11 installation, it will be installed successfully.

See if this helps resolve the issue,
Dan