I finally got over to Penn Station today for lunch, and stopped at the Baggage Office afterwards. A sign indicates that parcel checking is only available for ticketed passengers. I asked the baggage agent which tickets qualify. He said Amtrak and NJ Transit tickets only; Long Island Rail Road tickets are not acceptable. (How strictly the ticket requirement is enforced is something that I do not know.) I did not notice the rate for parcel checking, but I do not doubt that it is $5/bag/day.

FYI: NJ Transit one-way tickets are not refundable. The least expensive NJ Transit ticket is a one-way from Penn Station to Secaucus Junction. The one-way adult fare is $3.00; the one-way senior/disabled passenger fare is $1.50.