Are you priming it to make it start? If so it sounds as if it is just running out the priming fuel then stopping. If you are not priming it, then it sounds like a flow restriction upstream of the main jet: some garbage in the system, or perhaps the fuel pump diaphragm if it has the usual small Briggs engine tank-under-the-carburetor arrangement. You can verify that it is fuel supply by continuing to operate the primer after it starts: if it keeps running, it is a fuel issue.
If you can make those checks and come back, we can get a bit further. At the moment, dirt in a carburetor drilling or a faulty fuel pump diaphragm sound the most likely.
