Different APs and your main router are using different SSIDs? Try to fix different channels for all of them. What's the operating system of your laptop? To figure out where the problem is, you may...

You tried chipmaker's driver here? http://www.realtek.com.tw/downloads/downloadsView.aspx?Langid=1&PNid=21&PFid=48&Level=5&Conn=4&DownTypeID=3&GetDown=false&Downloads=true Did the try the latest one...

Remove all network profiles except the one with best Wi-Fi signal.

Maybe this instruction helps. Try to turn off the smart setup function on BT Home Hub 5. http://www.tp-link.com/en/article/?faqid=551 What's the firmware version of your WA890EA?

As I said, it should work as the modem is connected to WAN port.. So your router is not working normally. Sometimes, to configure a static IP on the PC may help to login its web interface and access...

Shorten wr740nv4_en_3_17_0_up_boot(150105).bin as wr740nv4_(150105).bin. And try again.