A new piston...with rings and a proper overbore + honing might not mean anything, 40 years later. If the engine wasn't stored properly, the cylinder walls could rust, so could a valve & seat. Most typically, compression loss is due to valves that no longer seal. You don't necessarily need a compression gauge to check compression. Turn the kickstarter by hand, slowly. If you feel sharp resistance on the compression stroke, that's an indication of decent compression. OTOH, if you have a tough time figuring out when then compression stroke is reached, ruh-roh. General rule of thumb sez bad valve(s) & seat(s) gives manifests as low compression, bad ring-to-cylinder seal as oil smoke. Normal compression readings 150-165 for a healthy engine, 130psi+ to get so-so power, 90-100psi minimum to get an engine to fire.
Since you've installed a new head, I assume that valve sealing is a non-issue and you've inspected the cylinder, so no rust or scoring is present. How about cam timing. If the cam sprocket is off by one tooth, the engine would barely run...making this a worthwhile item to verify, along with point gap.
No idea of your carburetor's condition, or even which carb it is. If it's new, it should be clean inside. When rebuilding a stock Keihin carb, the jets are usually replaced and the emulsion tube (which is also the main jet holder) is unscrewed from the main body casting, then every wall orifice carefully rodded-out, using a fine wire. Chemical cleaning alone will NOT suffice.
For now, try a few drops of gasoline down the spark plug hole, or in through the top of the carb (unscrew the cap) then seeing if it'll fire. If comes to life with more enthusiasm, then it looks like a fuel restriction problem. Obviously, it'll only run like this until those drops of fuel are used-up, a few seconds.
