6v or 12v, front or side distributor?
" I have other issues--the system will only turn over a few times before the battery gives up"
No, that is not an 'other issue'.
That is THE issue.
Weak battery = weak spark, as soundguy said.
You're on the right track to replace the cables & clean the grounds. While you are doing that, charge the battery. Then check it w/ a hydrometer (tip # 49)
But remember, while a hydrometer will tell you if you have a bad battery, it will not tell you if you have a good battery. Only a load test will do that.
You can do a 'shade tree' load test by checking voltage drop on a fully charged battery. Less than 5v means it's bad.
It's usually easier to pull it out & let the parts store check it w/ the correct load tester.