TL;DR: No because you are working full time.

30 hours or more is considered full time in NJ. But in context, I am assuming the job you are separated from is the typical 40hr a week shift since you didn't mention it. If you are working full time, no you cannot claim unemployment for a job you worked 34 hrs a week.

FYI, For partial unemployment, you can not work more than 80% of the hours of the job you are CLAIMING benefits for. Meaning, if you were working 34 hours at the job you were separated from, to claim partial unemployment you cannot work more than 27.2 hours a week at your current job.

Additionally, if you were to claim partial unemployment, then what ever you make (per week) at your current job will be deducted from your weekly benefits.

EDIT: Please don't listen to the "Give it a shot'ers". There isn't a dude sitting at a desk triple checking applications for accuracy prior to approval. Often times people who aren't necessarily eligible slip through and receive benefits they didn't qualify for. The last thing you need is your wages garneshed or your tax return seized because you didn't qualify for benefits (this happened to my daughter). Still unsure? Talk to someone in the unemployment office BEFORE you file.