Logan.....if you don't mind, could you put your location in your profile? Just the state or country would be all that is needed. As many members that we have on here, you may have a few members that are relatively close that may answer the questions better than others. Thank you.
Now, on the other hand.....when you say that you had an old octopus style furnace, I'm guessing that you have an old house, correct? Possibly built in the early 1900's? You also say that you haven't had problems until the utility room was built. To me it sounds like an air circulation problem. Other than the tiles (linoleum I assume) popping up, do you actually SEE moisture or water anywhere?
What type of walls do you have? Are they block walls, solid concrete walls, or stone walls?
What about your gutters? Has anything changed in that area of the house where the gutters have been changed, any other landscaping done around the house that might let water flow towards the house instead of away from the house. Does your downspouts all lead away from the house, or are they tiled into the ground? There are a lot of variables to consider when it comes to keeping a basement dry. 99 times out of 100, the problems with water in a basement has to do with no sealing of the foundation on the outside. It could be something simple, or it could be something complicated.
Can you post up a pic or two of the problem inside, in the basement, and then post up what it looks like at the affected area outside? It would help in making a determination as to the possible cure, which there are about a half a dozen.
Most want the lowest cost solution. That would involve sealing the walls from the inside with something like Dryloc or UGL.
Next you have the type of solution where they put a perimeter baseboard like deal around the base of the wall where it meets the floor. If it is a block foundation, they will drill holes in the bottom row of blocks into the cores, then put down a bead of caulk on both the floor and the wall, then put the plastic baseboard type of deal up, and finally it terminates at a sump pit.
The third way, is a company comes in, cuts the floor around the perimeter, they dig down, tile the perimeter pit to a sump, put gravel in, put some fabric cloth down, then concrete over where they dug out.
And lastly, and probably the most expensive, but the best way, is to dig down on the outside, seal the walls, Put a membrane over the sealed walls, tile the area, loads of gravel, and then finally backfill.
Sadly, there is no really simple solution to a wet basement. The cheapest is to run a dehumidifier 24/7/365, and have lots of air movement. But like I said, there are a load of variables as to which way to attack the problem.
The house was vacant for probably 5+ years. 
This is the only area moisture is coming from. Rest of the basement is dry. I might have to check for a crack. But either way is there something I can put on the concrete?