Can't log in after update

Yesterday my HD crashed on me. After a long frustrating day i managed to get it back and all files restored. However it reverted to the original OS the OS X instead of the Maverick OS, ok fine so i went to do the software update because none of the applications would work because my base OS is so old, but when the computer restarted it went back to the log in screen. Put my password in and it accepts it but it just goes right back to the log in screen after a few minutes. Please help! I really need to get this back up and running for school!!!!!