Remove the float and shake it. Any sound/ feel of liquid inside - you need a new float. If that seems ok, then replace the float valve and needle. It maybe possible that just a spec of debris is holding the valve open. Remove the fuel tank and rinse a few times w/ fresh fuel and also replace that 16 y/o fuel line while you're there.

Here is a link that might be useful: manual

You hit it on the nose because after I posted that message, I decided to disassemble the carb one more time. I removed the float and was going inside to see if it would float in water, and I noticed a swishing noise. Sure enough, it was full of gas. I've ordered a new float, gas line, and air filter (the one on there got soaked with gas).

The only question I have now is, will it hurt it to be laying on its side? If I sit it straight, it will obviously pour out gas, so I have it laying on its side. Will it hurt anything to leave it that way until I get the new parts?

Also, are there any maintenance issues I should address after fixing this problem since gas has leaked everywhere? i.e. change the oil? Thanks for any info!!

Use a pair of Vise-grips to clamp off the fuel line, and set it down flat. The oil will fill the muffler, and make it hard to start! hopefully, you have it sitting with the carb on the upside, muffler on the down side! The other way will cause oil to fill the carburetor, and then you will have a devil of a time making it run! BTDT!

I have it with the carb side up. The muffler is on that same side, so I'm not worried about that. Will it mess up anything internally?

It may fill the breather with oil. Then they act like a little oil pump and push oil in through the hose at the carb. MAy be good advice to run it initially w/o the air filter for a few minutes.

Success! I finally got all my parts earlier this week, and I got a chance to mow yesterday (it's been raining here alot), and it ran like a champ. I replaced the float, fuel line, and air filter. I may still change the oil, but it's running great now. Thanks for everyone's help!!

I have a Craftsman 917.388751 with a metal carb. I had the same thing, gas soaking the air filter and draining the gas tank overnight. I did a carb overhaul kit which included a needle valve seat. It said install the needle valve seat grooves side down and I thought that meant in relation to the ground which turned out to be backwards and it still leaked. I read a blog that said the carbs are so simple, they either work or they don't. I tore it back down, cleaned the heck out of it, installed a new needle valve seat, grooves side down into the carb, and now it runs like a champ with no leaks.