Water Heaters - Bad water heater? Not sure....

I think my water heater is going bad but I'm not sure - I can't figure out a way to troubleshoot it. Here's the deal...

Kenmore Power Miser 5 electric water heater, 52 gallon
Not sure how old, but label says warranty expires in 1997

A couple days ago we totally ran out of hot water which has NEVER happened in the 5 years we've been here. Checked breaker - heater is still getting power. Thought we had no water, but the next morning there was hot water - just not a lot. It ran out in about 10 minutes. Slowly got colder over that 10 minutes.

Is this a normal symptom of a heater going bad? Any tests I can do to confirm this?

Checking Sears' website, it looks like a 50gall electric heater goes for ~$249(house is on the market, so I don't want to spend a lot). How much does it normally cost to have it installed?

Thanks!

Couple of things could be wrong. May be one bad element and when it should come on it doesn't. Next would be the dip-tube is damaged or fell into the heater tank. You can check this by turning the power to the heater off and the cold water supply line. Disconnect the piping to the heater (cold water side) and unscrew the nipple that goes into the tank. The dip-tube "sits" in this opening and you can remove it with your finger. It should go almost all the way to the bottom of the tank. The way it works is that it takes the cold water to the bottom of the tank and thus pushes the hot water out. If it is damaged or missing, it "short circuits" the cold water right out the hot outlet. These can be purchased seperately. Check these things out. Good luck.