137 - The 1-51 may have a older model Tillotson, or an HL. Either way there's a pretty good chance one or both of the diaphragms are stiff. I have heard of soaking them in brake fluid, or steeping them in water with lemon juice to soften them up again. I know the water/lemon juice will soften them for a while anyway.
Also check the metering needle & seat to make sure it's clear. Sometimes simply priming and starting it a few times will get things going again.
triumph - In theory the spark plug wire is "screw" on to the terminal in the coil and can be replaced. Good theory, but I have a half dozen coils with twisted off wires that I haven't really tried to dig out yet. The 33/35 Series were pretty common, you should be able to find a replacement out there somewhere.
Mark