11yrs. old, it's a safe bet to replace the heating elements w/o worrying about wasting your time and money. I've seen heating element deteriorate and still yield continuity, I've also seen where calcium and mineral deposits give a false reading. The process is pretty straight forward. Turn off the water, drain the tank, disconnect the wires to the elements, screw them out, teflon the new one and reverse procedure. It's also and excellent time to drain and flush the tank (while the elements are out, bigger chunks don't go through the regular drain). I wouldn't worry about the dip tube until the heating elements are replaced as what you've described doesn't indicate a bad dip tube (you really don't want to deal with that 11yr. old can of worms if you don't have to, one step at a time).
Tip: Your going to get wet, don't fight it. Have lots of towels and/or a mop handy.
