I actually made a quick video of what happens on my side, I have turned off all pops-up blockers and such, so that shouldn't be intervering.
This is the Youtube Video I made
I wouldn't worry to much about the applications, big applications of that size generally crash a lot, though it's a bit interesting it just crashes before you even get a chance to log in or whilest logging in.
Thanks better than a screenshot.
Here is what I would suggest. Before performing these steps you might want to save your password and other login information used in the Need for Speed Network.
Remove cookies and Data site related to Need for Speed Network in Chrome https://support.google.com/chrome/answer/95647?hl=en
In the video I've noticed that you are automatically logged in when you go to the NFS Network App, this is the reason why I would like you to try this.
Also please unplug your router or modem from its power source for about ten minutes, then plugging it back in.
Can you tell me what's your service provider please, and if ever you've had the chance to try with another one?
Finally try to clear the DNS Cache: How to flush DNS Cache
The interesting thing seems to be that I've never actually managed to log in, nor tick the remember my details.
After clearing my DNS cache it seems to hold the website stable, it still does the 'automatic login', which is interesting because all cookies, webbrowser caches and remaining data... It stills auto logins in for a second and then clears up which allows me to enter my details.
The issue is that whenever I do manage to enter my details and hit login, it still gives me the exact same 'error 500'...
Further then that, I've tried all solutions which had no effect, for the different provider all I have to offer is a VPN, which I have access to, that should give the same effect, however it doesn't fix the problem.
Aside from clearing my browser information, DNS cache, reboot the router etc: I have a dutch provider named 'Ziggo'.
Can you then try this link: https://network.needforspeed.com/auth/origin in a new private browsing tab in order to prevent automatic login.
Also, maybe your Flash player is not up to date.
You can quickly check here: CHECK FLASH
For Google Chrome, see Enabling Flash Player | Chrome.
