The problem is, its hard to decide the definition of "resident"
According to the Bureau of Motor Vehicles: BMV: Indiana Residency Requirements
All you need is an address and be registered to vote. The State Dept of Revenue simply requires that you maintain a permanent address (your off campus apartment would suffice) and IN voting and DL.
Because of your off campus address, I think you could get your IN DL and register to vote, thereby becoming an IN resident. You would then be eligible for an LTCH. You would, however, be giving up your NJ residency. It's your call. I might be tempted to call the Indiana State Police to clarify, since they oversee the licensing process.
This is may be true but another thing to think about if you do this is if your parents are supporting you this can have adverse effects on financial aid...Just say'n
Proud Purdue parent myself.