I can't delete photos on my iPhone 4s even though the delete button is there, why? I've selected the photos I want to delete but, the delete button isn't turning blue. They were all taken on the iPhone but, the sim card has been removed. Do I need the sim card or not to delete the images?
SIM presence changes nothing. Even if you have iCloud photos you can delete photos without service or network and then those changes will only sync up once you connect.

Something else is amiss. Do you have a backup of the device and opportunity to test a restart / reset / restore?