I am an exempt salaried employee. My employer does not currently have enough employees to qualify for FMLA and no longer offers short-term disability. Under Indiana or Federal law, would I be entitled to receive full salary if time off was necessary due to illness or injury?

FMLA is unpaid leave, so that would not help you with income replacement even if your employer were subject. Since Indiana does not have a state disability program, and your employer does not offer one, unless you have purchased disability insurance on you own, I don't see any other options.