It sounds like from your description that you have a flashing leak and that could be fixed cheaply and effectively pretty well any roofer should be able to re flash (or seal the existing flashing).
If the masonry (bricks) are absorbing water then this too could be easily fixed by power washing them down and then applying a masonry sealer that is available at all masonry supply places.
About the only time I've seen bricks in need of replacing is when they start to flake apart.
As for if the chimney is an asset or not , call a real estate salesperson and ask them, if all your neighbors have one then your place might look silly without one.
Check to make sure the chimney crown (mortar cap) does not have cracks in it this is one of the biggest reasons for chimney leaks, also make sure you have a chimney cap fitted.