Updating firmware can't hurt, but I am befuddled about what is going on. Also try cloning the MAC address of the DIR-615, or even just changing it to anything but what it is (00:26:5a:x:x:x:x). If that doesn't work, I wonder if the router is malfunctioning somewhere at the firmware level.
Can you explain some more where you got the DIR-615 from? In OP you said you got it from your brother. Does your brother living in your apartment complex? Does he, or did he, also have Parknet for internet? I wonder if the D-link's MAC address is in there system somehow, attached to his account still, so won't allow access on your ethernet jack. A bit of a stretch for an explanation but it's all I can currently think of. TP-Link is also IPv6 compatible, unlike the DIR-635 so it rules that out as a issue too.
Did you still want to troubleshoot the issue or do you now just want to use the TP-Link router? Could I remote in now to look at the DIR-615 default settings and see if I can get it to work? Or have you email Parknet yet like they request? I don't think they would request you to contact them if they didn't think it was something they could fix. Not to say we might not also be able to fix it, it just might be easier for them. Please advise. :-)