Ordinarily, a Linux installation shouldn't affect your ability to use hardware in any other OS on your computer. The Linux installer shouldn't be touching files in the Windows partition. The installer will
resize the Windows partition, though, and I suppose it's conceivable that it's doing some damage to the filesystem in the process. A more likely explanation, though, is that the Mint installer is doing something to the boot loader configuration that's interfering with a computer-specific boot loader that's doing some hardware initialization. If the Mint installer removes that hypothetical tool from the boot path, then the OS drivers might not be able to use the hardware.
I can think of a number of possible solutions, but I can't be sure which of them will work, and they're all rather risky and/or tedious. The Boot Repair tool, mentioned earlier, is the solution that's most likely to get Mint up and running quickly, but it probably won't get the network functioning in Windows. For that, you'll probably have to either start again with a fresh Windows installation but get more data on its boot path or try to figure out what that boot path is based on the files that are present in your current ESP and/or other boot partitions.
If you want to start fresh, do so and then boot a Linux emergency system in EFI mode
and type "sudo efibootmgr -v" in Linux. (You may need to do a "sudo apt-get install efibootmgr" to get this to work.) Post the results here and don't proceed with Mint re-installation until you get the efibootmgr output interpreted.
If you want to try to repair what you've got now without re-installing Windows, try typing "sudo parted -l" in Linux and look for any FAT partitions. Mount each one in turn and search them all for files with names that end in .efi, as in:
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sudo find /mnt -iname "*.efi"
This example searches /mnt for such files. Those files are candidate boot loader files. Also, do a "sudo efibootmgr -v" to find out how the boot loaders are currently configured. With any luck, knowledge of the current boot loader configuration and of what boot loaders are available will suggest a way to reconfigure the system to get it working correctly.
Yet another option is to give up on a dual-boot configuration and run one OS or the other in a virtualized environment (using VirtualBox, QEMU, VMWare, etc.).