Are you sure the battery is dead. Did the starter just go click? If so you may just need to install a relay for the starter. It is a common problem. I still need to get one for mine. If I hit the key about 10 times it always starts. I will try to find the post on here that addresses that. I would not want you to buy a battery if you don't have to.
Congrats on the 1864!
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Travis
1993 Cub Cadet 2064
1988 Cub Cadet 2072
1980 IH Cub Cadet 782 w/CH20
1966 IH Cub Cadet 102 w/K301
1961 IH Cub Cadet O
1967 IH Cub Cadet 102 & 122
JD 2155 w/ 175 loader