Hijackthis and other applications should run as long as you are signed in as a user with Adminstrative authority. Don't ever try to install stuff in a Limited User account.
Whatever the infection is it could be preventing this too so try booting to 'Safe Mode with Networking' - tap F8 repeatedly while booting up and it's usually choice #2 on the menu.
If you still have MalwareBytes installed, update it and run it in that mode. Otherwise, install the FREE version from HERE, update it and run a full scan. Let it remove anything it finds and reboot if asked to.
Go to the Hijackthis website and try downloading it to your desktop also in that mode. If the installer balks because if infection etc. try renaming it in the process by using the 'Save as" option and rename it to 12345.exe or similar.
Reboot to regular mode and try running it in an Administrative-level account.
Do not post Hijackthis logs here, we can't help with those!
Post the logs at a specialist Forum:
Be sure to read all the sticky announcements/instructions at the top of each malware forum!