A 32GB SanDisk Ultra SDHC card should generally be compatible with a Canon 600D, so this is unlikely to be a simple incompatibility issue.

Based on the answers, the most likely possibilities are:

• the camera firmware needed updating (you’ve already done that),
• the card’s formatting/partitioning is confusing the camera, or
• the card itself is faulty even if another device can read it.

What to try:

1. Make sure the card is formatted as FAT32, not NTFS.
2. If normal formatting on a computer doesn’t help, completely wipe the card first (for example, writing zeros to the whole card, not just a partition), then reformat it.
3. If wiping the card produces input/output errors, the card is bad.
4. If other SDHC cards work fine in the 600D but this one still fails after a full wipe/reformat, the evidence points more to a bad or problematic card than to the camera.

Since your camera works with other cards, the camera itself is less likely to be the problem.