My landlord wants me to sign a new lease where I now don't have parking and she wants to raise my rent by $50.00. I'm not signing a new lease anyway so I'll be giving my notice.
After I give notice do I still have my parking until I leave or do I have to go by the new lease that she wants me to sign?

You are still under the old lease till the last date of that lease. They can not change the terms of the lease for the time frame of the lease.

So when does your current lease end ?
Are you staying past the end of the lease on a month to month basis or giving notice prior to the ending of your current lease to end on the last day of your lease?

Right now I am under a month to month lease. I signed a yearly lease in Oct 2006. It expired in Oct 2007. As of now I am month to month.

They can change the terms with a "30" day notice *** unless your lease gives a different notice time frame, some may say 60 day.
But they can inform you of any change in your month to month rental and it will take effect the next month. So if they tell you this month then in 30 days it will change in your rental agreement

Basic month to month rental