Some things to try first:
1. Turn Off your iPad. Then turn Off (disconnect power cord for 30 seconds or longer) the wireless router & then back On. Now boot your iPad. Hopefully it will see the WiFi.
2. Go to Settings>Wi-Fi and turn Off. Then while at Settings>Wi-Fi, turn back On and chose a Network.
3. Change the channel on your wireless router (Auto or Channel 6 is best). Instructions at http://macintoshhowto.com/advanced/how-to-get-a-good-range-on-your-wireless-netw ork.html
4. Go into your router security settings and change from WEP to WPA with AES.
5. Renew IP Address: (especially if you are droping internet connection)
• Launch Settings app
• Tap on Wi-Fi
• Tap on the blue arrow of the Wi-Fi network that you connect to from the list
• In the window that opens, tap on the Renew Lease button
iOS 6 Wifi Problems/Fixes
Fix For iOS 6 WiFi Problems?
Did iOS 6 Screw Your Wi-Fi? Here’s How to Fix It
How To Fix Wi-Fi Connectivity Issue After Upgrading To iOS 6
iOS 6 iPad 3 wi-fi "connection fix" for netgear router
Apple's iOS 6 Wi-Fi problems
How to Fix a Poor Wi-Fi Signal on Your iPad
iOS Troubleshooting Wi-Fi networks and connections http://support.apple.com/kb/TS1398
iPad: Issues connecting to Wi-Fi networks http://support.apple.com/kb/ts3304
WiFi Connecting/Troubleshooting http://www.apple.com/support/ipad/wifi/
How to Fix: My iPad Won't Connect to WiFi
iOS: Connecting to the Internet http://support.apple.com/kb/HT1695
iOS: Recommended settings for Wi-Fi routers and access points http://support.apple.com/kb/HT4199
How to Quickly Fix iPad 3 Wi-Fi Reception Problems
iPad Wi-Fi Problems: Comprehensive List of Fixes
Connect iPad to Wi-Fi (with troubleshooting info)
Fix iPad Wifi Connection and Signal Issues http://www.youtube.com/watch?v=uwWtIG5jUxE
Fix Slow WiFi Issue https://discussions.apple.com/thread/2398063?start=60&tstart=0
How To Fix iPhone, iPad, iPod Touch Wi-Fi Connectivity Issue http://tinyurl.com/7nvxbmz
Unable to Connect After iOS Update - saw this solution on another post.
Note - When troubleshooting wifi connection problems, don't hold your iPad by hand. There have been a few reports that holding the iPad by hand, seems to attenuate the wifi signal.
If any of the above solutions work, please post back what solved your problem. It will help others with the same problem.
The repeater does not create another network. It simply extends your existing network. The password needed would be the password you may have entered during setup of your main wifi router for wireless access. If you did not create this password then the router's wifi security was not turned on and there is no password to connect. If you have already been on your main network with a password no additional password would be required since the repeater would be a part of your main network.
You also have not answered whether you can connect to your main wifi router. Your repeater must be in range of your main network before it can extend it. So realistically your repeater should still be in a location where there is still a good signal from your main wireless network. Generally an area where the iPad may still have full signal or down one bar. You should also test with another wifi device such as an iPhone or a laptop, if they can not connect your repeater is probably too far from the main router.
You should also check the compatibility of your repeater. Not all wifi repeaters or extenders work with all brands of wifi routers. It is generally best to use the same brand of repeater as your main wifi router.