Sounds like there is (a) air in the lines or (b) a leak in the lines or (c) both.
Your lack of bleeder screws raises a huge red flag marked "danger" in seven languages.
The backs of your cylinders should look like
this and
this . If you have no bleeder screws, that's BAD. It's probably why you've got no pedal.
I would probably do 'ye olde brake job' to make sure that they didn't fail on me while I was driving it.
Either that, or make darn sure that my Emergency Brake Lever was hooked up and working.