@Starf81
When in doubt with any accelerator card, first of all ensure that all connections are completely clean. The motherboard edge connector, the accelerator card socket, SIMMs and their sockets. Dust, grease etc, some of which might even be virtually invisible to the eye can result in a flaky contact.
Cleaning with a cotton swab and some proper contact cleaner (or Isopropyl alcohol) can be a good place to start.
Also check the mechanical rigidity of the cards attachment to the motherboard, a slightly loose or wobbly card is a common source of problems, usually resulting again in a poor contact. Same with memory too.
Does your 1240 have a socketed ROM chip (the one adjacent to the SIMM socket)? Early revisions, like mine did. And a total pain in the arse it was too. If so, check it is seated firmly. Mine used to get pushed by the SIMM once installed and it is now as good as dead due to mechanical strain this caused.
I am not familiar with the 1D4/31kHz screen issue, so I can't really say.