You are lucky according to the map. Well, allow me to justify. Though you may have no service now, you have 100% guaranteed LTE according to that map. As such, TM are obliged to sort you out in any way they need to. I'm pretty sure this is a base station issue.
If you already have a support ticket, with no response from TM on mybb, then go to your nearest TM Shop and pursue things there. I know they have a direct line to a specialist support team which we don't. Take all evidence with you, printed out if need be, and hand it over to them.
Keep us updated.
Edit: with the coverage map you posted, please confirm the following:
1. Do you have an LTE provisioned SIM? Insist on another SIM card for peace of mind.
2. Do you know if your E5776 is configured correctly? Please post screenies of your config pages.
Note you are fast approaching the 14 day return cut off. You need to consider cancelling and then only renewing once your service has been sorted and verified.