Make sure you are not trying to install into programs files, also make sure your antivirus is not blocking the installition client.
another method that might work
Step 1: Uninstall Pando. If it's not in add/remove programs list, go to Program Files > Pando Networks > Media Booster > uninst.exe
Step 2: Download and install this: cdn.pandonetworks.com/pando/pmb/PMBInst.exe
Step 3: Download LeagueofLegends.exe from https://signup.leagueoflegends.com/en/signup/redownload
Step 4: Place file in a folder on the desktop named "League of Legends"
Step 5: Run the file as administrator