Cannot connect to WiFi in public areas or private or Ad Hoc connections

Question

I have a 32 GB iPod Touch 2G that is running 4.2.1
All has been going well, until last week. I tried to connect to a public WiFi (that I have connected to 50 times or more) and it said "Cannot connect to Network". I tried everything that I know how to do, but nothing worked. I then went to another public WiFi (with WEP), but could not get on there either. I then went home and tried to connect to my computer through an Ad Hoc WiFi connection (since we do not WiFi at our house), but I was not able to connect there either.
I reset it, I synced it, but the problem persists.
I always have the iPod on Airport mode, so as not to run the battery down. I then take it off Airport mode, turn on WiFi, and wait for the Network to show up on the iPod Touch. I then press the Network that I want. It immediately gives me the check mark next to the Network name, then later it gives me the WiFi symbol at the top left of the screen. I then wait for the Login page...it never comes up. I then go to Safari to force it to come up, but nothing. It says that I am not connected to a Network. I then get fed up with it and try to turn off WiFi, but the Network name stays, even though the WiFi is Off. I then try to turn on the Airport mode, but the airplane does not show up. I try and try to get away from the network, but it will not reset to normal until I press the Home button and the On/Off button together. I then get the circle of dashes (but just a short 1 and 1/2 rotations - ODD), then the black screen. Then I press the On button and get the Apple symbol. Then I sign in and the Airplane is there and the WiFi is off...till I try again. No connections and then I have to repeat this to get it back to half way normal.
Please help me with this situation. I really do not want to restore the iPod Touch, since I do not have a WiFi network near me...and I have a lot of apps that would have to be set-up through WiFi (taking a lot of time). My fear (if you could call it that), is that if I restore the iPod Touch, and find out that the WiFi problem persists...then I will not be able to use a number of Apps that I use a lot.
There has to be a simpler answer to this situation.

Answer 1

+Comment on #2. I'm not aware of any offline apps working with an iPod touch that hasn't been jailbroken. If you have jailbroken your device, we really can't help you here per the terms of service of this website. However, if this just updated data for a legit app or a web app, then it you are going to have to get network access working for it to work and, as you have said, iTunes isn't going to do it.+
Answer to #2: For one thing, the iPod Touch that I have is NOT jailbroken. I have never jailbroken any of my devices. I am a big supporter of Apple products, because they work. If a device is jailbroken, essentially taking Apple's expertise out of the equation. If I wanted to do that, I would use Android, and suffer with the fragmentation that they suffer with (along with all the problems jailbroken devices have). Enough on that.
Offline Wiki is an approved app from the AppStore (it is Wikipedia in your pocket, without the Internet). You download the app from iTunes. It is useless till you then download the content (whichever language that you want - for example the one I want, English is 3 GB of space). Since I am not in a WiFi area, and I do not visit WiFi areas often (nor for any real length of time, downloading 3 GB of information takes hours (nearly three hours, when I first did it). The only reason that I was reluctant to Restore my iPod Touch, was to avoid having to do that process again, and not being able to use the app (which I use a lot) until I do spend the time to download the Wikipedia Database onto my iPod Touch.
+A comment on #1. Those websites that require you to login again - this is a function of the network setup at that site. In effect, they are expiring your lease as soon as you disconnect. When you log in again, you are treated as a completely new user.+
Answer to #1: Yes, I understand that. Thank you.
Good luck on the restore.
Thank you. This, unfortunately was what I had to do. As expected, but not for sure, the WiFi is now working again. It seems that my iPod Touch got corrupted (within the iOS). The reinstalling wasn't as bad as I thought it would be, except I do not have the use of Offline Wiki (since my visit to the doctor yesterday was only for an hour, which I used to update all the other things that I needed WiFi access for. I started the download process, but it will take at least 2 hours to finish).
Conclusion: The only way to fix this situation, as far as I can tell, is to Restore your iPod Touch. Thank you for reading my long windedness. Also, thank you "luvlabs" for our conversation (though we haven't seen eye-to-eye much in the conversation, but I appreciate the time you spent to try. Thank you.
Message was edited by: Fr. Ignatius