This would include waterproofing over top of the existing slab, roll the membrane up the wall, terminate with batten bar, sealant, and butyl tape.

The sealant is expensive too.

Did a goggle search and see that sealant is the preferred method...Can I can do for alot less than $4K or do I have to have a licensed constractor do this?

I would think some type of sealant on the inside walls and a good de-humidifier along with double checking the downspouts on the house would be sufficient. 

The concrete floor doesn't appear to have any cracks from what I can tell and it looks like there was a sealant. 

He claimed there was some bandaid temporary sealant on it that needs to be "addressed".

Abatement or Remediation:  Many contractors will try to "sell you" on encapsulation, which is acceptable, (such as "painting it" with a recognized/certified sealant)  but leaves the potential there... and again it is ALL about disclosure...Abatement/Remediation is the more costly but permanent solution.... if is a roof, the roofer should be certified in the removal and disposal.

If the gap is not affecting your property in anyways, you can just seal it up with a sealant.

Let some of the chemicals and treatments dry out of the fresh lumber a couple of weeks before applying stain or sealant.

How in the h_ll did they get roof sealant on your bathroom fixtures?