It sounds like your current user account does not have administrative access on this machine. If you are attempting to install new programs you may need to do so from a different user account or set your current account to have administrative credentials.

If this is a home computer, and you are allowed access to an administrative account on this computer, you can alter the settings on your current user account by following these steps:

Open your start menu and select 'Control Panel'. Inside of the Control Panel window locate 'User Accounts', select User accounts to open the account manager window. Confirm that the account name listed on the right is the correct account for you, then select 'Change your account type'. This should open a new window, select 'Administrator' from this menu. If this account does not have administrative privileges you may be prompted for a password. Input the correct administrative password and confirm the changes, your user account will now have administrative access, which will allow it to install and modify programs and settings.

If this is a work computer you will need to contact a network administrator and request a change to your credentials.

Try saving the download rather than using Run. And use this download page to get the full, off-line installer package. https://www.mozilla.com/en-US/firefox/all.html