Good luck finding anything decent in that range. Anything under $2k is going to be rough. I have toyed with getting one for a couple years, seems like winter is the best time to buy. Last winter I saw a lot posted between $2000-$2500 that would have been good buys.
Facebook market is where you need to look every day. I see them show up in decent shape every so often at 1000-1500 but always need batteries which are going to run an additional 700-800. Anything under 1000 is going to be in bad shape.
An option that not many people think about is to call small town golf courses. Many elderly guys that get too old or pass away a lot of times sell their carts for a very low price. They don't really need the money anymore. I am talking little towns with 9 hole courses. These carts won't be very fancy but probably will be in decent shape.
Start reading the forums on Buggies Gone Wild. They have a classified section to buy carts and/or parts and a lot of guys who buy junk carts and turn them into beasts.
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