It is the same as other people experienced on Windows 7 that they can't able to use a higher version than 3.3.8.

If the Bitmover suggestion does not work your last hope is to upgrade your OS to Windows 10 which have better security, feature, and support than Windows 8.1(it will end support next year) and all new version of Electrum should be working as I tested them.

Can you tell us the reason why you don't want to upgrade it to Windows 10 since they already suggested it many times from old replies here? System requirements?
If it is just for the files then upgrading does not delete old files it should be still there on your hard drive after an upgrade.