I would not buy a second distributor because then you add retiming to the problems you already have. I would buy new points and condenser. ....one question, if you are using a remote starter swith to turn the engine over, did you remember to turn the ignition on to allow it to start?

'58 3600 350/4-sp/stepside/big window cab
'59 3100 235/4-sp/stepside