When I fire up KSP, the launcher will say "Looking for updates" rather than play or options, and the background will be a big red question mark rather than the Kerbal X Space craft. It worked just fine until now and I have had this game for a while. I am connected top the internet.
I had just purchased KSP a couple weeks before the update to 1.0. After a couple of days of the checking for update issue that you describe, I uninstalled KSP and deleted all related files.
I followed the down load instructions at the wiki and everything is now working fine.