I have no trouble connecting my Droid Maxx to WiFi and BT at the same time. I know that others are complaining, though.
Can you connect to WiFi with the BT radio off? How about vice versa?
If you restart in Safe Mode (long-press the power button to bring up the power off dialog, like usual, but then long-press the "Power off" on the screen and follow the prompts to start in safe mode.) If it works in safe mode, you probably have a third party application conflict for some reason.
Do you happen to have the app GasBuddy installed? If you uninstall it and restart the phone, does that fix the problem?
(These are just some issues that have come up in the last several weeks.)
What is your WiFi router at home? Is it 2.4 GHz or 5 GHz? Is it set for 802.11a, 802.11b, 802.11 g, 802.11 b/g, 802.11n, 802.11 b/g/n? 802.11 ac (I am pretty sure that the Droid Maxx doesn't support 802.11ac.) Do you have an open access point or is it secured with WEP, WPA, or WPA2? Have you checked if there is a firmware upgrade for the router that you haven't installed yet?
All that said, with the exception of safe mode/uninstalling GasBuddy, if had been working fine but suddenly stopped, it is probably a hardware failure. In that case, it sure wouldn't hurt to try a replacement phone. Or, of course, if you are eligible to upgrade right now, there are several good choices for upgrades available right now.
Good luck, I hope that you get it working somehow.