Disassemble the carburetor and give it a judicious cleanout using spray carb cleaner and compressed air.
You might also want to post the engine model number and the Craftsman technical model number (9 digit number under the seat).
Of course, if this machine has a fuel cutoff solenoid valve on the carburetor, that might not be working and could cause the same symptom you are reporting.
Take your can of "starting fluid" and throw it in the trash.
You should not use it on these light duty engines.
Spray carburetor cleaner is much safer (for the engine) to use as an alternate fuel by spraying into the carb throat when diagnosing fuel problems.

I had a similar issue. Check my thread from 3/17.

For what it's worth, if you are going to cite a particular post or thread, you should do it as a link.
When somebody stumbles across this a few years from now, 3/17 will not be very helpful. :^)

Here is a link that might be useful: Mohelpfulthanadateonacalendar

thanks for the tip, I can dig it. I just have to figure out how to do it!

This post was edited by Mocrazy on Sun, Mar 23, 14 at 11:21

I really doubt the "cure" from "3/17" applies in this case.
IF it were a bad key switch, it wouldn't run on starting fluid.

Easy Mocrazy.

Bill is just trying to keep the OP focused. As Bill described, the two problems have already been proven to be different since the OP has confirmed that his motor will start on starter fluid but will not stay running. If it was a malfunctioning key or switch the motor wouldn't even hiccup.