I bet it has the original 24 system on it. You need everything to be working correct for them to work right. Bad grounds and other wring issues are more troublesome on these systems. The trouble is the entire wiring harness and system is close to sixty years old. Lots of stuff that can be bad just due to age.
So you have options:
1) Fix the current system. That will take some knowledge/skill to do. More than likely the alternator is shot as the voltage regulator often gets messed up if there is a wiring issue. Also guys in properly jump starting them with ruin the alternator too. so this might be the cheapest repair but can still cost some bucks. Depending on how bad the alternator is smoked it could be $200 plus for just that alone.
2) Switch it over to 12 volt using the current harness. The Kits start at around $450 and go up depending on the quality of the starter/alternator in the kit.
3) Replace the wiring harness with a 12 volt one. Then use a 12 volt starter and alternator. This is the best way IF you can afford it and plan on keeping the tractor. Could easily cost $1,000 plus.