Car intermittently will not start

I have a 94 Achieva that runs great, but every once in a while I will go to start it and there is absolutely nothing, it is like the battery is dead, but all of the accessories and other items work.

I disconnect the battery cables and hook them back up and it will fire.

I have replaced the battery. Any other ideas?

i naturally start thinking of the starter, could be a selenoid problem, or the starter itself is on the way out, it could be something in the line, like a relay or fuse or something, but i dont know if starters have something like that.