Causes of slow spark?

Last night in the cold it was firing almost exactly 1 spark per second
Well that would be 120rpm on the starter, so I'm with Inkjunkie," weakazz battery"
If you try to jump it with another car or a known good battery, The dead battery acts like a big old sponge, sucking the electrons out of the booster just as fast as it can, leaving very little for the starter.
IMO you have four options;

1) during boosting, momentarily disconnect the dead battery just during cranking,, reconnecting it after she fires up.
2) pull the battery out, bring it in and warm it up for 24 hours, Top up the electrolyte, as may be required and then charge it for three days at 5Ah, on an automatic charger, or
3) In the event that the engine still cranks too slowly, Clean all connections between the starter and the battery, including between the starter and the engine, and the cable clamps to the cables, if they are separable.. And if that fails to up the cranking speed, replace the starter.
4) Buy/install a new or known to be good,battery.

But I have a quick test
With a known to be good set of booster cables, and with clean tight battery cables, including the cables into the cable-ends,you can hook one side of the booster-cables directly between the battery negative and the starter case.Use the black ones. This bypasses all the grounds. Then try it.
If still slow, hook the other cable, a red one, directly to the starter power-lug. Unhook the black jumpercable off the battery neg, and do hook the red one to the positive post. Finally re-install the black booster clamp to the Battery neg. The starter should immediately begin to crank at full speed. If it doesn't, check the integrity of all your connections, and retest. Still no good? replace the starter.

This assumes the cylinders do not have a buncha gas in them.An engine with some gas in it, cranks differently than when it's dry. And there comes a point it won't crank at all because liquids are not compressible. When that happens, the rod can bend.