Nexus 7 detects router but won't connect

[#1]

My brand-new Nexus 7 tablet has detected my router and I've entered the key but the tablet won't connect.  Onscreen messages seem to rotate between Connecting, Obtaining IP address, Saved, secured with WEP, and Avoided poor internet connection - that last one particularly baffling since the WiFi signal strength is described as excellent.
I'd be very grateful for any pointers as to what's going wrong and how to fix it.  Many thanks.
Bert

[#2]

Kind of obvious, but have you tried restarting the router?...
I've had no issues with mine connecting to a variety of routers, with varying levels of security...
Which router are you using?...

[#3]

Thanks for the answer.  Yes, I tried rebooting the tablet: it powers back up to the Select WiFi screen with the same rotation of messages - which I can't then escape from: does the Nexus 7 have to establish an internet connection before it moves on to its home page?
My router is newly-installed Plusnet Technicolour model and my connection is very fast and stable fibre optic.
Edited to add:
Sorry - I misread your advice.  I've rebooted the tablet but not the router.  I'll try that now.
Edited again to add:
Made no difference, unfortunately: though my desktop's connection is as good as ever, and my laptop's wireless connection to the router is working perfectly,  the Nexus 7 is firmly stuck on the Select Wi-Fi page.  I can't even forget about establishing an internet connection and get to the Nexus's homepage.  Frustrating isn't the word.
Bert

[#4]

You are not alone
https://www.google.co.uk/search?q=Nexus+7+tablet&oq=Nexus+7+tablet&aqs=chrome.0.57&sugexp=chrome,mod...
EDIT
Skimming through the above it looks as if trying different 802.11 standards may help
To try telnet into the router and then
wireless radio interop=802.11b/g/n for b,g and n
wireless radio interop=802.11b/g for b and g only
and so on

[#5]

@Bert, odd that it is secured with Wep. Normally the default is WPA/wpa2 for the tg582.
My nexus connects fine to one using WPA...

[#6]

Thanks for the new replies.  Before fiddling with the router settings I decided to try again - and this time the N7 picked up two instances of my WiFi network. I tried connecting to the new entry - and it worked! A Christmas miracle...
I don''t know why it's set to WEP, but since I'm not concerned about anyone hacking into the network where I am, and since everything is working, I'm content to leave well alone unless anyone feels that this would be a big mistake.
Thanks again and enjoy the rest of the day.
Bert