I've had the same problem which seems to have followed a recent BSOD.
I deleted the catalogue lock file (Located where the catologue is stored) and that appears to have fixed it.
Yes, look for a file in the same folder as your catalog. It will have the same name as your catalog but will have the lock extension. If you find such a file you need to delete it, and then Lightroom should start normally.
This "server busy" message is not catalogue corruption, and is not locking (Jim).
There is some problem with Lr on Windows which appears to relate to the licensing mechanism - see this thread and this. I have also suffered from it, at its worst a few times a day, but the message didn't happen every time I started Lr. Generally I just had to wait a few seconds and press Switch again, sometimes a couple of times, but it is annoying and worrying.
So my guess is that clearing the lock file wasn't relevant and in your case Lr simply started without triggering the error. Adobe have been working on the problem (I have been dealing directly with them) and since installing 6.1 / CC20015.1 I have only had the error message once.