Water heater plumbing question

I think that the dip tube in my water heater is busted: faucet water is less hot than previously (all faucets), and the inlet water pipe feels about as warm right near the tank as the hot water outlet. Gas burner seems fine (base gets hot, flame is visible), seems to cycle on and off reasonably.

Could the dip tube be responsible? If so, how do I get it off? The bottom portion of the inlet pipe with the nut is welded to the pipe, like they screwed the fitting to the threaded nipple, then welded the fitting to the rest of the pipe. Do I have to cut the pipe to unscrew the fitting? If so, can I then use a flexible hose with a compression fitting attached to the now-cut pipe?

That happened to us and it was the dip tube. Regarding how to get it off – no clue. We had someone come out and replace it.

http://www.ronhazelton.com/tips/faulty_water_heater_dip_tube_-_diagnosis_and_replacement

looks pretty easy if you can sweat a pipe. In this case the tube was falling apart so he was going to replace the whole water heater.