Any new 17lb (80 Newton) thrust engine will cost you more than twice your stated budget.
It might be possible to find an older (used) air start engine that can be had for something close to what you are hoping for, but you will also need to purchase a scuba tank and regulator in order to start it.
You might want to look into a kit built engine with onboard electric start.
If you go to: gtba.org you should be able to get more info on engine kits.

What are you using it for???