You should bill the guy who sold you the deep cycle as a starting battery.. Now the good news.
If it's a Marine/Deep Cycle (not a true deep cycle) it should work.. If it does not,, Try cleaning the connections (This fixes mine every couple of years) as Marine/Deep cycle are really starting batteries, Just not rated for below freezing weather (Still work though).
The engine battery should be a regular starting battery though. Deep cycle are designed for a slower (relative to total capacity) discharge... Of course, since a pair of six volt is like over three times a group 24 capacity wise.....
The starter load on the house is a "Slow discharge".
Home is where I park it!