your wheel either has a cassette or a freewheel, they are not the same. since it's old it's almost certainly a freewheel. that means you can't take it apart and remove cogs like you describe, that only works with a cassette.
a)take it off with the appropriate tool,
b)try to pry it off with something (probably wont work)
c)go to the park tool site and read about destructive freewheel removal,
d)just wrap the chain around whichever cog yields a straight chainline or
e)replace the wheel.
those are your options.