It still seemed to be flaky about temperature, and I noticed the lower element dripping, so I decided to attempt to drain it by allowing the water to pour out from behind the lower element. It took forever since it is a 50 gallon tank and I had to use a baking pan to bail it out. I had to use a bunch of towels to catch the water that I missed in the pan. Once I finally got it drained we got a better look at the element. It was VERY corroded and did fork out, which the replacement one did not. I took a channel locks pliers and squeezed the element together and it bended easily. I had to continue crimping it to get it out. When it finally cleared the hole it was so corroded that the metal had disappeared in several places and the wires were exposed. The corrosion must have caused it to fork out.
From the hole of the lower element we could look in and the whole bottom of the tank was full of calcium deposit flakes which is why the drain faucet would not flow. It's crazy how hard the water is here. If I had to go back I would have definitely invested in a water softener for this house when we bought it.