Curious about something. When I boot up my laptop using the hdd, the wireless card isn't recognized. It doesn't even show I have one installed. Now for the curious part. The wireless card does show up when I boot from a thumb drive. Any ideas why this occurs?
No idea from the information you give, could be several different problems my first guess is incompatibility of the wi-fi or drivers not loaded..
open a terminal, type inxi -Fnx
scroll down to the section headed Network
highlight the whole section then paste it in this thread.
I forget and I'm don't have my Mint system immediately to hand - plus it's LMDE. Does Mint need proprietary software, which would include wireless drivers, enabled? If so, look there. It may be set to work in a live environment but need to be enabled after install or maybe during the installation phase.
In Mint there are several cards Broadcom and Realtek for two that need additional drivers installed.
If you can connect via Ethernet cable or tether to a smartphone you can check the additional driver manager and install the needed driver in that way. If It's realtek it you may have to download the driver and build it first. see here for more info.
Also in addition to the command that brickwizard gave you please execute this command and post the output here.