this sounds more like network problem than a linux one; but since you're using linux w/o an internet connection, you'll have to use the tools that usually come with Linux:

start with basic information. see if your computer has an ip address and who its primary gateway(s) is/are

ip a
ifconfig -a

if you see no ip address preceded with the word "inet" these commands (127.0.0.1 doesn't count); your computer doesn't think it's connected to a network and the source of your problem is somewhere with either the hardware, driver or mint itself.

if you do see an ip address with the word "inet" in front of it; then use that basic information to start troubleshooting; these commands are a shortcut; duplicate information; and should be run in order:

for i in $(netstat -rn | grep ^0.0.0.0 | awk '{print $2}') ; do ping -c 3 -W 1 $i ; done
if [ $? -eq 0 ] ; then cat /etc/resolv.conf ; traceroute google.com ; fi

this command provides duplicate information but provided here in case mint has really weird packages on it

for i in $(route -n | grep ^0.0.0.0 | awk '{print $2}') ; do ping -c 3 -W 1 $i ; done
if [ $? -eq 0 ] ; then cat /etc/resolv.conf ; traceroute google.com ; fi

if neither of the last 2 stanzas worked, then your computer doesn't think it's connected to a network that has internet access and you need to figure out what's up with your network or fix routing on your computer.

See the network icon on the right-hand side of the bottom panel? What does it show when you click it?

• Is there a "Wireless" section?
• Does it have an activated checkbox next to it?
• Is there a little circle to the left of your wireless network name?
• And what percentage is showing for the link strength?

If the "Wireless" section is missing, go to the main Mint menu, run "Driver Manager" (under "Administration"), and see if it finds a WLAN driver for you. A working connection in the live environment isn't necessarily transferred into the installation.