Another photo since I don't know how to post 2 pics in the original post. Oh, and I clean the floors with Bona for hardwood floors.

you need to get a wood floor cleaner from a flooring store. Unsing water and Dawn is not a recommended way to clean your floors. The Dawn is likely to leave a residue. Talk to a flooring store not a box store.

Ancient floor wax? It certainly looks like crud, not something you want on your floor. The finish appears intact in the upper picture, the floor looks like it may not even be stained. Stain would be under the clear finish in any event.

Dawn doesn't leave a residue, that's why they use it to clean birds after an oil spill. Does require rinsing though. Water with some vinegar added seems to do the trick at a fraction the price of some specially labeled cleaner.

Agree about Dawn...makes a great eyeglass cleaner, rinses clean and leaves no residue. However, for floors...I don't know.

The previous owner may have applied a sacrificial coating, or as rwiegand suggested ..."wax" or some other acrylic polish in an attempt to make them look better prior to a sale.

Keep working to remove the offending layer.

it appears to be a residue from a wax, perhaps the previous resident used a wax type floor cleaner that dried and left a gummy gross layer I would continue your regime until you have removed it all then continue using Bona for your regualr care. The previous members are correct, your stain is under the clear urathane sealant so you are not removing it, and Dawn does not leave a residue, remember to use alot of clean water wipes after to remove the soap though and be extra cautious in any event to get minimal liquid between your boards while you are stripping the scum off and follow with a dry rag don't leave it wet with water or cleaner at all!!!!!!! With regular use the shine will eventually return I'd imagine. Cleaning the scum migh dull the top of the urathane layer but the rubbing buffing of wear should shine it up again.

I respectfully disagree with anyone saying that Dawn doesn't leave a residue. Maybe it doesn't leave a residue when you uses it on dishes but if you're going to use it on a floor, it needs to be rinsed well. Better not to use it at all. You're better off using Bona cleaner since it's alcohol based.
Dawn is used to clean oily birds because it cuts grease well and is gentle on the skin.
http://www.npr.org/templates/story/story.php?storyId=127999735
The problem with your floor is likely that it has layers of self polishing wax. The usual culprits are Mop-n-Glo and Orange Glo. These can be removed with non-ammoniated wax stripper diluted in water but it needs to be done carefully since it is a harsh chemical and it can harm the wood. We usually do most of the work by hand and rinse it well after stripping.
Another commonly used polish is Bona Polish. Bona makes a polish remover.
Judging from the second picture, your floor is worn in the grain allowing water to enter the wood, causing the grain to turn dark.
I would suggest you get a professional to look at your floor. It may be time for professional refinishing.

thanks everyone! I will keep scrubbing and eventually get someone to look at it to see if it should be refinished.