Adobe's customer service isn't equipped to help you with IT issues like dead computers or network problems. They deal mainly with installation and billing issues and also can't really help with "how to use the software" problems, which is why you're being sent to the forums.
As for the blank account page, make sure to turn off any advertisement or pop-up blocking add-ons you may have in your browser when viewing Adobe's sites, especially the store and account areas. I've had several locations in their site fail to load due to either Ghostery or AdBlocker, pausing or turning them off while on their site fixes that issue for me.
If you don't have access to the old HD, to get your site files back...
1. From your new copy of DW, go to Site > New Site
2. Add the site's name and browse to a folder you want to use as the local root
3. Click Servers
4. Click the + to add a remote server
5. Enter a server name and add your FTP info from your hosting company (don't forget the server Root Directory)
6. Test the connection. If it works, Save
7. From the Files window (F8 or Window > Files if it's not open) click the Get (down arrow) icon
8. When asked if you want to get the entire site, click Yes, sit back, sip some coffee and wait for the download to finish
9-?. Rinse and repeat for each site you had on your old computer