It's almost a certain that the out building will be on a different ring circuit to the house so won't work with any kind of speed.
You say running a cable is impossible, is there no fence or wall a cable could be tacked to?
Proper way: cable and access point.
I wouldn't bother with a wireless link but the above suggestions might be fine.
^ Not very helpful - are you suggesting koolpc terminates the cable himself?
110 ft is about 30 m, I would grab a 30 m run ready made, search ebay for something like "30m external cat5e", some good looking cables on there for around £10. (Longer is fine if you want to play it safe, up to about 100 m.)