You need to work out where the problem lies - so you need to establish exactly what you still have access to when the WWW stops:
Check network settings - IPconfig /all in windows, whatever the equivalent is in your flavour of linux: check the IP address, gateway & DNS servers are valid.
Check the DHCP pool, number of assigned addresses, lease time and scope options (i.e. DNS server, gateway, etc.)
Check for internet access restrictions on the router.
Ping gateway IP address
Ping another device on your network
Ping DNS server(s) given by ipconfig
Ping internet IP address - e.g. 8.8.8.8
run tracert (or linux equivalent) to the external addresses
Ping internet host name - what error do you get? does it resolve to an IP address?
You should be able to narrow it down to an internal error or an upstream problem.
If you can use a wired connection with a static IP address and fixed DNS server that will eliminate some of the potential problems. Note that you would need to ensure that the static IP is outside the DHCP pool.
Your ISP tech support is pathetic, BTW - "the problem is linux mint" - what bollox.
If you have done a factory reset, you should change the admin password from the default, if not already done, and set your own wifi PSK (password).