old gas is old gas. the fuel stabilizer should have prevented it from turning to a varnish like substance and gumming up you fuel system.......but it is still old.
if that does not fix the problem, I believe you have a fuel delivery issue.
I am assuming when you say it has spark....it has spark, and I also assume your compression didn't go away over the winter. all that leaves is fuel.
unless you live in Alaska, the normal oil for all Harleys is 20w-50.
in any case....you need 4 stroke motorcycle oil.
if you can't find it locally, buy it off the internet.
do yourself a favor and do not put standard automotive oil in your Harley.
** it is ok in a pinch, like if you find yourself in the middle of nowhere and need a quart of oil to get home.....but never do that on purpose, for convenience **
your petcock (fuel valve) is also vacuum operated. drain the old fuel through the petcock by attaching a vacuum test pump to the vacuum line nipple on the back of the petcock......this will help you verify the vacuum petcock is operational.
let me know what you find.