I was partly right once, so perhaps the luck (ahem) will continue.

Barring a bad part, it sounds -- as someone else suggested -- that there's
something wrong with the board, or a solder joint.

Lemme tell you a story...

Back in 1980, I assembled an Integrex kit and had problems with one of the
op amps overheating. I spend almost an hour checking voltages, resistances,
etc, trying to figure out exactly what was causing the problem.

It then occurred to me to turn the board over and look carefully. Viola! Two
traces had a solder bridge. (Integrex was cheap and didn't provide a solder
mask.)