Be curious whether the router is working properly or not. firstly, make sure the internet is working on the router. You may check the internet with other device.

Try the following link: http://www.tp-link.com/en/article/?faqid=306

Seems that you have already tried many methods about adapter. You may try to change wireless channel on your wireless router.

Try the following: http://www.tp-link.com/en/article/?faqid=463

Use windows utility to connect wifi not TP-LINK utility. Or you may remove TP-LINK utility and only install driver of the adapter. Besides, try to change wireless channel on your wireless router to...

Soft AP help you transfer wired connection into wifi connection. Very confused why you have old WEP connection. There is no security of wired connection..... Certainly, you may install utility to...