In a word: yes. If you have been offered admission to a graduate program, but have not been offered funding, it is not a crisis situation. You should begin your school regardless.

If you have started graduate school without funding, you can always apply each year. You should apply for grants and assistantships (both research and teaching) each year. Some grant applications are due in early fall, so be sure to check out the deadlines of any to which you are going to apply. It might seem that you have only started school before you have to get your funding applications in.

Once you have begun your studies at a school, you have an advantage over those applicants who will be entering next year. You will know professors and be able to get references that count. Applying for funding twice will help show the department and the granting organizations that you are dedicated.

Remember that your school isn't the only organization that can offer you funding. Check out your government websites (municipal, provincial or state, and federal) to find grant applications. Look at other organizations such as businesses, charities, and social groups that fund scholarships and grants each year.

Even if you can support yourself and pay your tuition by working during school, take the time to apply for grants and assistantships. It looks great on your resume, and will help you in the long run.

For the meantime, when you are trying to fund your first year of studies without help from the school or from outside sources, consider getting a loan to pay for your studies. You can get specialized loans designed for students, for graduate students, and sometimes even designed for particular fields of study!

Having a loan instead of working long hours will ensure that you have the time to complete the applications (which is very time consuming: it will take you days to get all of the materials written, your references gathered, your transcripts and other supporting documents). It will also mean that you are free to devote yourself to your studies. Demonstrating a keen attitude and enthusiasm for school will help you stand out in your professors' minds. You want them to notice you, to respect you, and to help you get the teaching assistant or research assistant position that you are looking for!

In the end, if you truly want to go to school, you will be able to do it. Just carefully assess your funding options, and never give up on applications. Apply each year, and apply faithfully. It might not be fun, but in the end it could be what ends up paying the bills.