Can you look in device manager and see if it says Broadcom driver
?/belkin wireless card
If you pull your belkin 7001 and physically look at it (for your piece of mind) on the shielded 'tuner' side there is a huge black chip in middle of card - mine say's "Broadcom"
If it's the 'Broadcom' version mine worked straight off (32bit) - no worries as far as I remember.
Some Belkin 'g' 'g+125Mbps' cards have 3 or 4 revisions all using different manufacturer chipsets like Broadcom/Ralink etc.
Ralink are very good at keeping drivers
up to date with all versions of Windows/linux - have a look on their website if you have Ralink chipped card as there are special Windows 7 versions on there.
I updated my card to a (Ralink chipset) Linksys/Cisco WMP600N Wireless 'n' pci card (Ebuyer-UK) £30inc post
coz I was having poor reception problems with my G+ card (over a period before Win 7 too) & couldn't be bothered waiting for Belkin free replacement hassle - so I have not used the Belkin for a couple of months.