Startup sequence with FileVault enabled: Initial login screen actually unlocks the disk. OS loads after this. So, the Mac is shutting itself down at som point while the OS loads. Without File Vault, the login screen appears at the end of the sequence rather than the beginning...
What version of the operating system?
What model MacBook Pro? (If you don't know, at least tell us whether it has a built-in optical drive.)
Is the Mac backed up? With Time Machine?
Have you got an external boot drive? If so, then run a
SMART check. If the drive passes SMART then
boot to Recovery, unlock the disk with the Disk Utility, and then quit the Disk Utility and re-install the operating system right over the existing install.
If this gets her booting then 1st thing I'd do after logging in is
run a malware scan.
If it doesn't work then take it to the Apple Store (don't forget to make an appointment) and ask for an
Apple Service Diagnostic check. NOT just "VST" which is what they'll want to do.