Barry,

I think your going to have a rough go of it without the presision of at least a table saw. Finish nails are not going to cut it and 1x4's are going to also cause you some hate and discontent. Number one, the 1x4's are not going to be sturdy enough without adding so much cross member and joist support, that your storage space is all used up. I'm assuming you were planning to put a sheet of plywood on top of the frame for the box spring to rest on. and you would probably want another one on the bottom for your storage containers. You could come up woth a descent enough frame set up with 2x4's and ply, your biggest problem is going to be appearance. With some very careful planning you could come up with something servicable, but you'd make life much easier with a table saw. Don't mean to sound negative about the project, but with limited tools, this will be a tough one.