I tried using a new SD card on my Kodak EasyShare C360 but the camera doesn't functions

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What size is your SDXC Card? The maximum supported it 2 Gb. It can't handle more than that and won't format.
https://kodakassist.freshdesk.com/support/solutions/articles/48001068427-what-size-and-type-memory-cards-can-i-use-in-my-kodak-digital-camera-

EASYSHARE C-Series Cameras accept:

• C1450, C1550: SD and SDHC memory cards up to 32GB
• C300, C310, C315, C330, CD33, CW330, C530, CD40, CD50: SD memory cards up to 1 GB
• C340, C360, C433, C503, C533, C603, C633, C643, C663, C703, C743, C875: SD memory cards up to 2 GB
• CD43: xD memory cards only
• All other C-Series Cameras: SDHC and SDHC UHS-1 memory cards up to 32 GB

https://www.memorycow.co.uk/digital-camera/kodak/easyshare-c-series/kodak-easyshare-c633-digital-camera#:~:text=Your%20Kodak%20Easyshare%20C633%20Digital%20Camera%20is,2GB%20Micro%20SD%20memory%20cards.

Manual

Kodak EasyShare C633 Manual

https://kodakmanual.com > kodak-easyshare-c633-man...
EasyShare C633 Camera User's Guide PDF File - Kodak EasyShare C633 Manual Table of contents: 1-Setting up your C633 camera ....1; 2-Taking pictures and ...

....

This requires a SD memory card. I would stay with 512 mb or smaller.

If you just purchased this camera, you can try phoning place of purchase or make a trip there. It sounds as if the software in camera may be messed up.

No. You cannot use a 8GB SDHC card in the C360. The C360 supports MMC and SD cards up to 2GB in size.

Get another memory card. The C360 works with SD and MMC cards, not with SDHC cards. While an SDHC card will fit into the slot, it is electronically incompatible.

The C360 uses MMC and SD cards. Your 4GB card is actually an SDHC card. While SDHC cards will fit into SD devices, they are electronically incompatible and will not work. You need to use SD cards 2GB and smaller.

The following information lists the type and maximum storage capacity of the memory card that each type of camera accepts.

EASYSHARE CX-, DX-, LS-Series Cameras accept:
DX3500, DX3600, DX3900: CF memory cards up to 1 GB
LS755: xD memory cards only
All other CX, DX, LS: SD memory cards up to 1 GB
EASYSHARE C-Series Cameras accept:
C300, C310, C315, C330, CD33, CW330, C530, CD40, CD50: SD memory cards up to 1 GB
C340, C360, C433, C503, C533, C603, C633, C643, C663, C703, C743, C875: SD memory cards up to 2 GB
CD43: xD memory cards only
All other C-Series Cameras: SDHC and SDHC UHS-1 memory cards up to 32 GB
EASYSHARE M-Series Cameras accept:
M590, M583, M577 TOUCH, M5370 TOUCH: MicroSD and MicroSDHC memory cards up to 32 GB
All other M-Series Cameras: SD, SDHC, SDHC UHS-1 memory cards up to 32 GB
EASYSHARE P-Series Cameras accept:
P850, P880: SD memory cards up to 2 GB
P712: SD or SDHC memory cards up to 4 GB
EASYSHARE SLICE Digital Camera accepts:
MicroSD and MicroSDHC memory cards up to 32 GB.
EASYSHARE V-Series Cameras accept:
V1233, V1253, V1073, V1273: SDHC, SDHC UHS-1 memory cards up to 32 GB
All other V-Series Cameras: SD memory cards up to 2 GB
EASYSHARE Z-Series Cameras accept:
Z610, Z650, Z700, Z710, Z730, Z740, Z760, Z7590: SD memory cards up to 2 GB
All other Z-Series Cameras, including MAX: SDHC and SDHC UHS-1 memory cards up to 32 GB
FUNSAVER FD-Series Cameras accept:
SD and SDHC memory cards up to 32 GB
EASYSHARE ONE Camera accepts:
SD and SDHC memory cards up to 1 GB
Notes:
Most KODAK Digital Cameras are compatible with SD, SD/MMC, and/or SDHC memory cards.
Most current KODAK Digital Cameras are compatible with SDHC UHS-1 memory cards.
All KODAK Digital Cameras that are compatible with SDHC and SDHC UHS-1 memory cards use cards with Speed Class up to Class 10.
MicroSD and MicroSDHC cards with SD adapters can also be used in cameras that use SD or SDHC cards if the storage capacity criteria above is followed.
KODAK Digital Cameras are not compatible with SDXC memory cards.

reference: http://www.kodak.com/global/mul/service/index.html?reqURL=http://support.en.kodak.com/app/home/src/gosupport

http://support.en.kodak.com/app/answers/list/p/2/selected/true

Phone Number for Kodak is:

800-235-6325

or try get human below for more info on support:
http://gethuman.com/phone-number/Kodak/

Is the slide switch on the side of the card in the unlocked position?

The I would have to say bad card. Do you have another to try?

If you used the SD/MMC memory card in another brand of camera or device, you may need to format the card in your new EasyShare digital camera. (You may have noticed a "Memory Card Needs Formatting" message when you inserted the card.) CAUTION: Formatting deletes all pictures and videos, including those that are protected. Removing a card during formatting may damage the card. To format the SD/MMC memory card or the internal memory of the camera: Transfer images to the computer before formatting the memory card. Press the camera Menu button. Highlight SETUP MENU, and then press the OK button. Highlight FORMAT, and then press the OK button. Highlight an option - MEMORY CARD (deletes everything on the card), CANCEL (exits without formatting), or INTERNAL MEMORY (deletes everything in internal memory). Press the OK button. Highlight Continue, and then press the OK button. Wait until formatting is finished before removing the card. When formatting is complete, the SETUP MENU is displayed. Press the Menu button to exit the menu.