Lenovo had to supply you with a way to reinstall the Operating System when you bought the machine.
That can be in the form of a Recovery DVD or a Recovery Partition on your Hard Drive, from which you were supposed to make Recovery Disks from.
"Lenovo recovery gave me a disc, and said I would have to install other components myself "
That doesn't really explain what they have given you to work with.
I can only suggest that you try it.
If it was the correct Recovery Disk that they gave you for it, you should not need the Product Key (read my first reply about that)
We can't help you with a Product Key.
And Microsoft no longer sells Vista.
Cheers.