By resetting the switch you are also sending a reset to the connected computers
When they refresh with their static IP or DHCP IP, they are probably ok for 10 mins before any Malware take over again.
To confirm this scenario, you could leave the switch on and reset the computer, if you get 10mins again, then again it's not the resetting of the switch that is helping here.
I also note you are using: FileZilla
FileZilla is an FTP program for file uploading and downloading to and from your FTP site, server, or host. The program lets you transfer files and navigate among folders, Web sites, and your computer. This software enables you to perform multiple file transfers simultaneously.
Although FileZilla is possible the safest of all sharing programs on the Net, it is still a file sharing program. If you don't need to "File Share" to users on the Internet, I feel a Server environment should not have it installed
Regarding format.
If you decide to format, then I would suggest to remove the Partition
Partitions can be easily corrupted from Windows System files and Malware infection
So go with the remove Partition
all the time
By the way, if you are re-Partitioning, then you may as well try the Norton removal tool
You might just get Internet working perfectly all of a sudden.