Okay, here's how I ran the cable from the basement to the bedroom TV. I think it will work for the majority of MOCers:
Drill hole near existing water lines, or if you want to be precise, measure from where water lines enter the bottom of the cabinet to where you see a 3 inch by 2 inch carpeted box. This carpeted box is actually an iron box tube with wood on top. The bedroom dresser drawer rear sits on this carpeted box.
Insert your cable into the bottom of the bathroom cabinet and then into the end of this carpeted box tube:
Now shove your cable to the end of this tube after carefully cutting the carpet away on the opposite end a few inches from the stacked drawers on top of which sits the bedroom TV. Drill a hole in the top going through first wood then iron. Chamfer the wood horizontally towards the stacked drawers so that when you put the cable in this chamfer, the carpet will lay back nicely. You might want to add some adhesive to the carpet:
Now, remove the bottom drawer and drill towards your chamfered spot in the tube. Insert cable through chamfer and hole and then run up to the TV!
Took me and my DW about 30 minutes once we figured out how to run the cable.
I hope this helps other MOCers.