Your Fire TVs and the Recast DVR need to all be on the same network and logged into the same Amazon account to work properly. If you changed your Amazon password, this might cause some of your devices to not work properly.
You'll want to start by logging in to the Fire TV app on your phone/tablet. When you load the app, it might ask you to log-in again. Go ahead and do that with your new Amazon account information.
After that, you will want to restart the Fire TVs and the Fire TV Recast. Start with the Recast. Since it's not working right, you will need to just unplug it, wait 10 seconds, and plug it back in. It's the black box with the one light on the front. Next you can reboot the Fire TV Stick:
Reboot Fire TV Stick: Settings > My Fire TV > Restart > Restart
There are other ways to reboot the Fire TV stick as well.
Reboot Fire TV Stick with remote shortcut: Hold down the center "Select" button and the Play/Pause button at the same time for ~5 seconds and it will reboot
Reboot Fire TV Stick by unplugging: Unplug the small micro-USB cable from the side of the Fire Stick, wait 20 seconds, then plug it back in. Note: Unplugging the Fire Stick from the TV does not reboot it.
That should get things working again, but if not, you should reach out to Amazon tech support for help, as StreamWise Solutions does not have any access to your Amazon account.