Welcome to the bureaucratic red tape of college! You also picked a less-than-ideal time to try to start this up, since this is the craziest and most busy time for registrar/bursar/financial aid, etc. But, don't let that discourage you from continuing. I've dealt with two colleges in Chicago to finish up my second Masters degree (Chicago State and Northeastern) and the lack of communications between offices was baffling! So, I'd say your experience is pretty normal.
Things that might be helpful in the future:
#1 - Most schools will have a definite 'fall' and 'spring' semester. You can usually learn about class schedules and begin the registration process a few months in advance - highly recommended. Don't wait until the week or two weeks before or you might run into closed classes and absolute chaos (as you experienced).
#2 - Financial aid should be applied for as soon as you receive your W-2 forms in the beginning of a calendar year. You will want to fill out a FAFSA form. To make a long story short, the government takes a look at your assets and liabilities then determines how much money you have available to pay for college. An example: Let's say you want to go to a school where the tuition is $5000. According to your FAFSA, it is determined that you will pay $4000 per year. The remaining $1000 will be funded by 'aid', either scholarship/grant (you never have to repay it) or loan (you eventually have to repay it). Keep in mind, this is just a simple explanation. Sending in the forms and having them examined takes a while, which is why the registrar/financial office told you that you should have done this previously. In the future, as long as you're going to school, fill out the FAFSA as soon as you get your taxes done. Packages begin rolling out no earlier than March or April (there is a definite 'beginning' date, but at the moment I forget when it is).
Good luck to you and don't let the confusion of the various offices discourage you from continuing. Just make sure you keep EVERY receipt, EVERY piece of paper, and document every phone call etc. so that when someone in the office screws something up you have proof!