They we're not lying if they told you it was a 64 bit machine if they were talking hardware.
If your machine has a 64 bit processor and the chipset to support it then it should run a 64 bit OS no problem.
If the chipset supports it 64 bit Win 7 should see all 4 GB of your installed ram.
It is possible that even with the 64 bit hardware you still won't be able to see all ram.
Example: my Acer Aspire 5672 WLMi came with a 32 bit Intel core duo processor but was upgradable to the 64 bit Core2Duo mobile processor
when it became available a few months after I purchased it.
I performed the processor upgrade but Win 7 64 bit still only "sees" 3.0 GB of my 4 GB installed ram.
The chipset is the issue. The chipset used by Acer doesn't support recognizing 4 GB or more of ram even though the processor is 64 bit.
A later Intel chipset does.
I doubt if the above circumstances apply to your machine but it could explain why it shipped with Vista 32 bit.
You might try running a free 64 bit Live Linux CD like Ubuntu and see if it can see all your ram.
If it doesn't then 64 bit Win 7 probably won't either.
That's what tipped me off, I installed a 64 bit version of Ubuntu in a dual boot to try to utilize all my 4 GB ram.
The most it would see was 3 GB.
A 64 bit Ubuntu Live CD .iso can be had here.
Download | Ubuntu
Burn to a CD using the instructions on the page.
If your machine can boot a USB thumb drive use the instructions for USB.
It will create a much faster Live experience.
Boot to Ubuntu Live and when you get to the desktop there will be a space above and below with icons (linux calls this a panel).
Right click a blank area and choose "add to panel".
Scroll down to the System Monitor applet and highlight and OK.
A little rectangular item will appear.
Clicking it will show system info including the amount of available ram.
If it shows less than 4 your machine can't address all ram even though it's 64 bit capable.
I'm assuming you don't know much about Linux so don't take offense if I'm wrong here.
A live CD\USB won't make changes to your system, it runs entirely off the media it's installed on (either CD or USB device).