Wake up from sleep

Having struggled to get my computer to sleep -

When I do a wake up from 'Sleep' I get - Windows did not shut down correctly.
It then offers the 'Safe Options' list,

Anyone know why it does this?

Does the power remain connected to the PC?

No, once in the Sleep or Hibernate mode I turn the power off.

You cannot turn off the power while the computer is sleeping. It needs to keep the RAM powered up to remember the information to resume. That is why you are getting the message that Windows did not shut down correctly.
You can turn off the power for hibernation however, since the resume information is written to the hard drive.

Windows 7 also has a hybrid sleep mode that lets it go to sleep but also stores the resume info on the hard drive and if the power is turned off, it will resume as if it were hibernated

Ok I have turned 'Hybrid Sleep' on,
I can now turn off the power on both Hibernate and Sleep...

If I have done it right then thank you for that..

You can turn the power off, just remember that returning from hybrid sleep after you remove power is just as if you put the computer in hibernate only.

Sleep is typically used to shut off most power (just a small amount is used to keep the RAM powered) if you would like the system to come back up quickly so that you can continue right where you left off.