RESIGNING DUE TO ILLNESS OF FAMILY MEMBER
I was laid off in July 2009, in April 2010 found a job paying much less but close to my new home (I moved from NYC to Upstate NY). Now I just found out that my mother is extremely ill and will not be able to work; hence, I am going to move back to the city so I can support her and be close to her. I will need to resign my present job to do this and move back to the city and find a job there. My unemployment still shows up with a balance when I login. Is this considered a good cause and what are the chances of collecting unemployment? I worked for 9 years straight in my previous job, have been six months in my present job.
Length of your previous employment is not relevant .. except that you have a balance on the claim.
However, caring for a sick relative can be good cause, but the thing to look out for is being found not able and available for work. Usually, medical documentation showing the need for care is essential, but the reason you stated for quitting was your mother's financial hardship.
If quitting for such a reason is necessary, I would suggest first seeking an FMLA leave or at least a personal leave of absence from your current employer. Otherwise it is a quit for personal compelling reasons only and not attributable to the employment.
Try the NY unemployment interpretive index
for more reading material on the subject.