Exactly where were the DLLs installed?

If you had previously done "just for me" and then this time did "all users", the python27.dll for 2.7.17 will be in C:\Windows\SysWow64, which has lower priority than the one in the same directory.

I won't be fixing or even reviewing any issues in the 2.7 installer at this point. If someone else identifies an easy fix, they're welcome to merge it, but if the problem was changing the mode of install then I'd rather leave this as user error (and be thankful that we've reduced the likelihood of that error since 3.5).