Sick Atari STE wisdom sought

[Gordon JC Pearce]

I've got an Atari 1040STE, which was previously working (well, after I
blanket-resoldered the PSU - always a notorious spot for dry joints).
After leaving it for a while, I came back to find it had locked up with
the desktop showing, but not responding to keys or mouse.

On rebooting I get a blank white screen - locked, but just blank - and
the floppy drive doesn't spin up.  Nor do I get keyclicks when I press
the keys.

What could I look at first?  With the ST come up with the keyboard
unplugged, or will it just sit there in silence?

Gordon