Locked screen stays on locked screen

Resetting the PRAM may do the trick:
You reset the PRAM by rebooting a Mac and then immediately hold down the Command+Option+P+R keys, you will then hear the Mac reboot sound again, signifying your PRAM has been reset. You must hit the key combination before the grey screen appears otherwise it won't work.

you've tried rebooting, you've reset the PRAM, you've done it all, but your Mac is still behaving strangely. What next? In certain circumstances, resetting your Mac's System Management Controller (SMC) can be a solution. This is sometimes necessary to restore normal lower level system functionality to your Mac.

Here's how to reset the SMC on any type of Mac (and any version of OS X) and the type of problems that it may resolve.
When & Why Reset SMC on a Mac? Some Common Hardware Reasons

Typically it's power and hardware related issues that can be helped or resolved by resetting a Mac SMC, particularly if you're having these types of problems:

* Issues with your Mac's cooling fans and fan management: fans run constantly at high speed, fans run high despite low CPU usage and adequate ventilation, fans not working at all, etc

* Power management and battery problems: Mac isn't turning on, sleep isn't working, random shutdowns and reboots, battery isn't charging, Mac won't wake from sleep etc

* Light problems and improper lighting management: battery indicator lights aren't working, display backlighting isn't adjusting to ambient light changes, keyboard backlights not working, etc

* Video and external displays not working: display brightness functionality not working properly, target video mode isn't working properly, external display isn't working, etc

* General performance and functionality problems: abnormally sluggish behavior despite no CPU or disk usage, external ports not working, airport & bluetooth aren't showing up, external devices are not being found, etc

So now that you've concluded you need to reset your SMC (Note that the SMC is on Intel Mac's only), here's how to do it on MacBook's, MacBook Pro's, iMac's, Mac Mini's, and Mac Pro's. Notice that the reset instructions are different for MacBook and MacBook Pro's if you have an internal or detachable battery.
Reset SMC of a MacBook Air, MacBook Pro Retina, or MacBook Pro's with an internal non-removable battery

This is how to reset SMC on most modern Mac laptops:

Shutdown your MacBook Air / MacBook Pro
Connect the power adapter to your Mac
On the MacBook/Pro's keyboard, hold down the Shift+Control+Option keys and the Power button at the same time
Release all keys and the power button at the same time
Boot your Mac as usual

Here's the key sequence to hold down:

Reset the SMC of a MacBook Air or Retina MacBook Pro

Do keep in mind that by resetting the SMC you will lose power specific settings, like the time it takes to sleep a Mac and other customizations to power settings. No big deal, but if you have made many changes to your hardware behavior you will want to adjust stuff like sleep behavior again.
Reset SMC of an iMac, Mac Pro, Mac Mini

Resetting SMC is different for non-portable Macs:

Shut down your Mac
Disconnect the power cord
Press and hold the Mac's power button for 5 seconds
Release the button
Reattach the power cables and boot the Mac as usual

Reset the SMC of a MacBook or MacBook Pro's with detachable batteries

mac reset the smc Older MacBook laptops with a removable battery can reset SMC with the following approach:

Shutdown the MacBook/Pro and remove the battery
Disconnect the power adapter, hold the Power Key for 10 seconds
Release the power key and reconnect your battery and power adapter
Turn your Mac on
Let boot as usual

Hopefully that will clear up your problems, if not it might be worth a visit to the Apple Store or a certified repair center.

Happy New Year,
Kerry