Are you getting no power at all or just now power to the radio console?
There isn't a lot that can go wrong when changing the air filter. But If you didn't plug the connectors back into the ECM and Cruise properly then you probably won't get any power to the ignition. FWIW I managed to leave those ECM connectors alone when changing my filter but it was a tight squeeze and I think next time I will disconnect them to avoid the risk of stressing or breaking pins or wire.
It seems like you will be pulling the shelter up to check those connections. Let us know how it works out for you please.
This might sound a tad obvious, but would the battery be flat or a terminal knocked loose? Have you checked the connection under the Meter Panel? More than one GL1800 owner has forgotten to reconnect that one.
Can you post a picture of the white connector? It sounds like one of the connectors for the CB radio filter, but I'd need a picture to be sure.
There is nothing under the shelter that would have normally been disconnected to change the air filter. I don't even disconnect the ECM, just pull it out of the bracket and lay it back with the harness. There is a red unused connector if it doesn't have heated seat and grips.
I did have an incident with mine when changing the air filter. After getting it back together it wouldn't start, lights worked but nothing when I pushed start. I took it back apart, looked, scratched my head, what did I do? Finally found I had accidentally turned the kill switch off. I never use it so it just didn't ehter my mind.