I opened up the drywall around the area and saw that it's coming from the dranage pipe of the upstairs sink.

If you are thinking striking down lead regulations to reduce your costs, it may be counter productive.

But I called the realtor, and was talking to him and he told me that the house has "broken water pipes".

Either the AC isn't working, or the hot water heater quit working, or a pipe burst, and on and on.I've thought about dropping these two properties because the trouble isn't worth the money I make on them.

I've seen more than a few times a 2x10 sistered on to the old 2x6 joists that dropped the ceiling height another 4 inches, and 2x6s  used to raise the floor to be level across while still being able to run piping/hvac below.If you don't have the cash to do it right, I'd say just leave it as is since either way it'll be a fight with the city if they find out.

There is a company that will resurface both the cabinets and the counters.

Does this type of lender exist or is it a pipe dream?

They can always counter.

I know to check pipes (on city water so water should be flowing), but any key points I may overlook?

I'm thinking something dark because the counter tops are light.