There are several possibilities that could be blocking the install from completing. You may have to institute several of these solutions in order to get the installation to complete:
Is this a shared installation, as you may need to go into the tools link on the main screen and install using the Shared Installation option available under there?
Do you have all of the required prerequisites installed on the system? (You can find those environment requirements for each version here: https://hpln.hp.com/page/alm-qc-enterprise-technical-specifications )
Do you have pop-up blocking for Internet Explorer (IE) turned on? If so disable it (it is under the tools menu for IE)
Are you using the IE browser ? (as only the IE browser on a Windows system will allow the desktop installation ,and it must be both IE on a Windows environment due to the active X components not supported in other browsers and operations system environments)
Do you have the UAC (User Access Control within the Control Panel) disabled (turned down to ''Do not notify'' the lowest setting)?
Is the account being used to install the desktop client an account that has admin privileges (or at least the full read and write permissions for the folders needed to install the client, check the install guide for those file locations if you need to check that)?
Close IE and then right click on the IE icon and select the ''run as administrator'' option when initially launching the browser to do the intial install (after that it shouldn't be necessary to run as admin).
Also add the site to either the trusted zone or local internet (I prefer trusted zone) to insure things aren't blocked. You may also try savingt the installation file to the desktop and running from there instead of selecting the Run option.
Also make sure that the dialog boxes aren't maybe being hidden behind the browser (as sometimes they pop up awaiting user input and are net easily accesed.
Lastly you can try to install the ALM Explorer (it is under the tools> utility add-in sections for ALM, accessed from the tool link on the main landing page). I have seen installing the ALM explorer can install some of the necessary files and allow the browser installation to complete successfully.
These are many of the common resolutions for such issue. If after trying these and nothing has resolved the issue, you may want to open a case with your support group to get assistance to get this resolved.
Hope this helps,