Ok lets try 2 more things. if that doesnt work then i will need to remotely connect to figure out what is going on .
CLick apple icon
select system preferences
select users (or accounts in earlier versions)
then Click the plus icon ( underneath the list of users)
and select to make a admin user
you can use whatever name you like as long as it is not the same as your current user
then click ok
select the apple icon and select sign out
and sign in to the new account
is it the same?
Turn off your mac then hold the shift key. Turn on your mac continuing to hold the shift key for no less the 2 minutes.
then try to install.
1. turn off mac
2. Locate CMD and R keys
3. Turn on mac holding the keys from step 2
4. You will see a bar fill once this happens let go of the keys. A menu will pop up and there you will see Disk utility.use disk utility to repair hard drive by clicking verify disk. Then reset.
5. Once its done resetting we can attempt to reinstall the osx