Hi OP. I use Peapod religously even thought sometimes they really suck. I just hate going to the grocery store and love the convienence of shopping online.
If you call or email Peapod and let them know of the issue, they will refund the money right away.
A few orders ago I ordered two 18 packs of eggs. One pack - half the eggs were lose in the grocery bag. The other pack - half the eggs were broken in the carton. Got all my money back and kept the eggs that were okay.
As for how long the eggs will keep, check out this link:
http://stilltasty.com/fooditems/index/17144