You need an industrial epoxy applied by a professional. If the concrete is old enough.And there is a vapor barrier and insulation under the slab. If not, then you need a different surface entirely.

To decide what material works best, you will need to have an epoxy professional come in a do moisture/RH/pH testing on the concrete. Once the test results come in, then the professional can then choose the best material to apply to your concrete. You would choose a clear epoxy to maintain the look you have right now.

What did you decide?

This helped us understand options for basement concrete

http://www.vseal.com/blogs/classroom/12781285-choosing-a-sealer-penetrating-vs-topical