Windows 7 supports exFAT ( http://en.wikipedia.org/wiki/ExFAT ), I suspect the problem is that you have an SDHC / SDXC card but your card reader can't handle it. What is the make/model of the card reader that you are plugging the SD card into?
BTW, SDHC/SDCX look physically identical to SD cards, but can hold more data. Specifically, SD cards are limited to 2 GB total capacity (that's the entire card, not individual files), so you definitely don't have a straight, plain SD card.
Response to Additional Details:
Yes, I believe all you need is an SDHC-compatible card reader. If you're currently trying to use a laptop/monitor with built-in card reader, then try going to the manufacturer's support page for the laptop/monitor and downloading new drivers -- I know my laptop 'gained the ability' to read SDHC via a software update*. My particular monitor, on the other hand, will never be upgraded this way, the manufacturer can't be bothered releasing the upgrade. It's just luck of the draw.
SDHC is physically and electrically identical to SD, it's just the SD protocol that can't represent sizes above 2 GB (kind of like a Y2K situation.) So it's a basic software fix to upgrade to the SDHC protocol, but the device manufacturer must have implemented it first.