If I work 17 weeks per year @ 24 hrs per week and the balance of the year at 40 hrs. or more per week, am I classified as a "part time employee or full time employee"?

Full time

Its not that simple. If your schedule was changed to full time, then at that time your classification should have changed. If, however, your schedule wasn't changed, but they had extra work for you beyond your schedule, they might still classify you as part time.

Why is this important?

For purposes of the Affordable Care Act ("the ACA," also known as "Obamacare") anyone scheduled to work an average of 30 hours per week is considered full-time, and so is covered by the employee mandate. For other purposes "full time" employment does not have a standard definition but rather is defined by the company, and is typcally spelled out in the employee's handbook. For most companies (not all) anyone scheduled to work at least 32 hours/week is considered full-time, which may qualify them for full-time benefits such as vacation accrual and retirement benefits. So talk to your HR department to see how they define your employment given your odd schedule.