1998 Chevy Express Blower motor runs with key off

The blower motor for heat/air all of a sudden started running on its own today, even when the key is off, draining the batteries. Fan speed switch and off/heat/ac switch have no effect. I can sometimes get it to stop by turning key on (to clicking w/dead batts) then off. Then it comes back on by itself within a minute or two (perhaps because of a slight movement making relay/module/resistor defect again?)

A little history:
- Van has experienced both severe cold (-32F, Fargo ND) and desert temps (over 100F - southwest US) over the years, though temp today when it started acting up is 50F.
- AC has never worked in the 5+ years I've owned it.
- Windshield has leaked, and moisture getting into dash did cause radio display to act up a good while back and still does, but everything else has run normally. 'Til today.

Bad blower motor relay, resistor, module? Which to check first? Other suggestions, or what I should tell garage? Can do myself as fairly competent shadetree mechanic?

Any help or advice is deeply appreciated. Donation sent.

Thanks!

'98 Chevy Express 3500 - 1 ton van w/6.5 turbo-diesel