Here's a Blower-Doesn't-Run portion of a troubleshooting checklist which I think applies to the 8516-IV...
Also-
- what thermostat are we talking about?
- what does the control-board LED show during yes-it-works vs now-it-doesn't runs? The LED is on the board so the outside cover has to be off to see it. I don't know if it will light at all but if it detects a problem it will flash or turn on with a solid color. There should be a sticker on the motor cover area showing what the flashing codes mean. They're a little cryptic but may give us a clue.
- you say you checked connections-- including the one to ground (I vaguely remember yellow wire going to a short ground bar tucked up under on right side. Does that make sense?)
- If I remember correctly the relay on my '01 8516-IV was obvious and looked like the one in the components-identification portion of the manual. And there's a test or bypass procedure for it. But I also remember reading something about the relay being moved or incorporated in the board so yours may not have an obvious one.
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OK will check. Thanks for the help.