I've considered having the entire set graded, but I think that would cost hundreds of dollars. Plus I'm on the east coast and PSA is on the west coast (I think), and being without any experience in the grading/shipping process leaves me a little hesitant to follow through. Thanks for "guesstimation" though, it's much appreciated.
It does take a little work, and it may cost you a few hundred dollars to get the set graded but if they truly are nm, you will get many times your investment back.
I just joined PSA & sent in a bunch of diecuts recently that I thought were nm, and most came back psa6. It really makes you appreciate the 7s and 8s. It is a fun experience, and they do have good customer service for getting your questions answered.
If the set is ungraded, most (60% to 70%) of the value will be in the Ratz & Cracked. Aside from the Ratz & Cracked, sets of diecuts in nice shape have typically sold for around $1000 on ebay with alt titles in place of Ratz & Cracked. If these 44 titles are 7s or 8s, you could expect $50 (for 7s) to $100+ (for 8s) (and more for non-repeat titles) so that would make the value $2200 to $4400 aside from Ratz/Cracked. Not a bad return on a few hundred dollar investment. Problem is, most raw "nm" cards don't turn out that way after they are graded.