I had an interesting time helping someone that could run PChat, but not the QChat add-on. I got into his hard disk and searched EVERYWHERE for his City of Heroes files so I could re-install PChat and make sure the pointers were pointing to the right files. Turns out they were in Documents in a folder named 'New Folder'! So, I ran the PChat installer with the '-nux' option (causes the installer to ignore any previous installs and install as new) and of course, it didn't find the files. I renamed 'New Folder' to 'COH' and ran it again and it didn't find the COH files, so I used the Browse option to point it to the \Documents\COH folder. It identified the files as I24 and installed without error. Then I downloaded and installed the QChat mod and it ran perfectly.
So, if Qchat is not installing, locate the COH files, rerun PChat install with -nux and point it to the COH files you found, and then install QChat.
NOTES: Exit PChat and COH. Turn OFF your antivirus while installing (and you may have to tell it later to not test PChat so it won't block it).