To be extremely specific about the things you've tried -- probably most of this, but, on the off chance. . . .
On the fire: toggle wifi off and then on.
'forget' the network, and then re-enter it
If it doesn't find it on it's own, you may have to manually enter it -- especially if, for instance, the network name isn't broadcast.
With wifi ON, turn OFF the kindle and then turn on again.
Unplug router. Plug it in again.
Check password for typos (lower case 'L' and the number '1' mixed up, or letter 'O' and '0' (zero))
Our 'resident expert' Morf will no doubt be along after a bit, but it is possible the router is not compatible. Yes, it should be, but others have had similar problems as well, especially if the router in question is fairly old and/or an 'off' brand.
You can definitely transfer content via a home computer, but can't connect to the internet on the Fire through a computer. And you will need to connect at least once to complete registration. Might be easiest to go find a public hotspot and do that there. Unless you're in an extremely rural area you should be able to find some eating establishment where you can get a coffee or something and use their wifi for a half hour.