Does the brain have a theoretical limit as to the amount of information that it is able to store? For example, if an average man/woman were able to achieve immortality or live an extremely long time (50,000-100,000 years) would there be a point at which the brain would no longer be able to process new memories or would it just start “writing over” older memories?
Yes, but hopefully the DVD burner standards will have been resolved and you store all the data you want.
I forget. I used to know, but I can’t remember now. 
From various sources on the web I got these figures:
2.6 billion neurons in the cerebral cortex, where most of the higher brain functions are located.
10,000 interconnections per neuron.
So if we call 1 interconnection 1 bit (and I know I have no right to do that, but it should work as an upper limit) we get a total capacity of 26 trillion bits, which about equals 3250 terabytes. Unless I goofed my arithmetic.
There is definitely an upper bound to the amount of information that can be stored in any given amount of matter. However, nobody really knows how to measure the capacity of the brain, so we can’t say how long it would take before a person runs out of space.
Surely there would only be a problem if the person was endowed with immortality and total recall; surely the bits of my brain that used to contain memories of all those things I’ve genuinely completely forgotten aren’t gone; memory gets overwritten doesn’t it? (in a manner of speaking).
No one knows.