Thank you for the pictures!
All right. There is corrosion on it and thus it is recommended to replace them!
First, you need to de-solder those from the motherboard and solder new ones back in.
Second, the battery cover need to be replaced as well.
You can get the battery springs here: [link|https://www.aliexpress.us/item/3256806158111191.html?spm=a2g0o.productlist.main.1.7eed2926FYozo7&algo_pvid=5f02d923-bde6-406d-8635-3b33204e33bb&algo_exp_id=5f02d923-bde6-406d-8635-3b33204e33bb-0&pdp_ext_f=%7B%22order%22%3A%22161%22%2C%22eval%22%3A%221%22%7D&pdp_npi=4%40dis%21USD%219.58%213.07%21%21%2169.16%2122.17%21%402103867617461746010044812e332f%2112000036832610135%21sea%21US%210%21ABX&curPageLogUid=7vmBedoIvXsb&utparam-url=scene%3Asearch%7Cquery_from%3A|5Pairs For xbox 360 Replacement Wireless Controller Battery Springs - AliExpress|new_window=true]
You can get the battery cover here: [link|https://www.aliexpress.us/item/3256806587260334.html?spm=a2g0o.productlist.main.2.4f702746tSmvg6&algo_pvid=82026404-7416-464f-ab2d-2195e1089264&algo_exp_id=82026404-7416-464f-ab2d-2195e1089264-1&pdp_ext_f=%7B%22order%22%3A%2214%22%2C%22eval%22%3A%221%22%7D&pdp_npi=4%40dis%21USD%214.92%212.59%21%21%2135.50%2118.66%21%402103849717461745728886247ee636%2112000038255489372%21sea%21US%210%21ABX&curPageLogUid=XXThyCV3xT2V&utparam-url=scene%3Asearch%7Cquery_from%3A&_gl=1*1ev6fb5*_gcl_au*MTQ2NDAxOTAyLjE3NDQ3ODkxNzg.*_ga*NDAwNjQ1NjAuMTc0NDc4OTE3Ng..*_ga_VED1YSGNC7*MTc0NjE3NDUzNS40LjEuMTc0NjE3NDU3Ni4xOS4wLjA.|2-4pcs For XBOX360 Game Controller Battery Back Pack AA Battery Holder Cover Case Replacement for Xbox 360 Wireless Gamepad - AliExpress 44|new_window=true]
If you have any more questions, please let us know!