About multiple applications for graduate programs to the same school
This is a very good, but very difficult question. The problem is that there's no definitive answer here. 

What we do know:


You turned down a previous offer. This is never helpful for future admissions at a given school.
You were not able to accept because you weren't qualified to start. So long as you clarified this with the school in question, this may be a mitigating factor.


What we don't know:


How the school evaluates candidates. Is it a "rolling" admissions process, in which candidates are considered year round, or is it done on an annual basis?


The last point is probably the most important. If it's a rolling admissions, and you were a high-quality candidate in the previous cycle, you'd probably have a good chance of getting admitted, provided you explain what happened and why you couldn't get in.

On the other hand, if the admissions process is done once a year, then you will have to compete against all of the other candidates in this year's pool. Then, it's not necessarily a given that you would get in having gotten in previously. If you were a "bubble" applicant last time, You may be below the "cutoff" given a different pool of candidates—or you could be a clear admit.