I'm using VSEW 2013 and running windows 10.
I created a login page (Login.aspx) and a signup page (SignUp.aspx). I used the standard controls and did not add any code behind to them. They are out of the box controls.
Looking at your web.config, for some odd reason this section is there:
<system.webServer> <modules> <remove name="FormsAuthentication" /> </modules> </system.webServer>
This section coupled with the fact that your authentication mode is set to forms:
<system.web> <authentication mode="Forms" /> ... </system.web>
Would make it so that authentication wouldn't work at all, which is like what your describing. Try removing that first section, if you want to keep using Forms Authentication.
It's odd that this configuration would work on other computers, I can't explain that, but I would try removing that section of code where FormsAuthentication is being turned off and see if that helps.