Windows 3.1 (and WfW 3.11) do maintain an uptime counter, but it is only available by an API call so you need a program to see it. If you can get it on the machine then this will tell you what you want to know.
EDIT: Apparently that one isn't the correct file, here is a different one I found that seems to be correct, the original reference I found was here.
Supposedly from command prompt you can run net statistics server
and see the start time of the computer, but it's buried and with no grep
command in Windows it is hard to find.