First thing: think of the hard drive as your storage. Think of "memory" as RAM. It may help to imagine the two as being like a file cabinet and a desk: the hard drive is your file cabinet (where files are stores and where they are "saved" after being worked on) and RAM as your desk (the larger the desk, the more documents and tools you can pull out of the "file cabinet" and work with).
So you say your hard drive is full? If that's so, then that's why your computer won't start up -- it needs room to operate and you've deprived it of that. Assuming the drive hasn't crashed outright, you're going to need to take the machine somewhere where someone can boot it up from an external drive, and help you remove the excess stuff that's filling up the drive to capacity. Once that's done, the machine should work normally.
I don't mean to be blunt, but if you're not going to make the effort to learn some MINIMAL maintenance and "best practices" for using your computer, you're going to have problems over and over. You wouldn't buy a car without learning to drive it, running it without maintenance until finally the oil gave out and the engine blew up, would you?
Macs are great in that they don't need a lot of attention like a PC does, but that doesn't mean they don't need ANY. And working without backups -- on ANY platform -- is like ice skating on a frozen lake on a sunny day. I would respectfully suggest you take the effort to learn a few basics about your machine --
Mac 101 is a good starting point -- and once you get the machine fixed up, buy an external drive for backup as well as a larger-capacity drive for the machine you presently have.