I think your question is : do you become eligible for unemployment benefits after a 45 day period even if you were denied benefits because you quit your job? the short answer is no- you must appeal the denial of the finding that you quit your job. If 45 days have passed, you may be past the deadline for appeal. Further, there is the question whether you have any way to show that you did not voluntarily quit. should you speak to an attorney, the question to ask is whether the circumstance of your leaving the job give you any factual basis to challenge that finding.
This is general legal advice and is not intended to establish any attorney client relationship.