Just to get my head around this, your setup is:
Modem -> Router 1 (old) -> Router 2 (new)
The date is incorrect on number 2 (it should get the time/date automatically? [unless it's too far out
])
And you are having WiFi/password issues with number 1?
Is the WiFi working correctly with number 2, you can connect to it, and are you able to change the password with out issues?
It sounds like the new password is not being saved when you change it. Are you sure you are changing it on the correct router?
Also, are you aware that the modem also has an IP address, and you have taken this into account when setting new addresses for number 1 and 2? (and also the IP address range for DHCP?)
Other than double checking everything you have done (it does sound like it's setup right) then it could be an issue with the router
I have a new router coming from ebay. I guess if I replace the old one, it will work then on two separate passwords?
The new-new router would have it's own SSID and a password and you can change this to whatever you want.
If you remove the existing router from your setup you will need a new password to access your new-new router. The old WiFi/password will cease to be and no longer work.