For a while now I've been almost certain this is the case. Definitely, at some point, malware on my stepkid's laptop gained access to the home network and managed to change some settings.
Router is a
Not an easy way. I would recommend downloading and installing the latest firmware for it. The exact file will vary depending on the version of DIR-615 you have. After doing that I would recommend that you:
Doing these things will help secure your router, but in the event that it is compromised you should be able to compare the settings with your backup copy and verify your DNS is going through Google or OpenDNS.
Yes, your router can be mangled by malware, either by settings getting changed, or even bogus firmware loaded into it.
If you believe it has been hacked, take the possibly infected computers off the network, then reset the router to factory defaults and then change the admin password and disable remote administration. If there are firmware updates available, download and install them, again making sure that the admin password is different from default and remote admin is disabled.