I use a Belkin USB bluetooth adapter on my computer to communicate with my Sony T610, and it was fairly easy (this is not to rub the salt in).
I don't know whether my Belkin bluetooth software is the same as yours. But having installed the Belkin software/drivers, I don't need any further software to connect with the phone. (Even the Nokia site doesn't suggest that you need the Nokia PC suite.)
I don't know what steps you've taken (and you may have used the bluetooth adapter successfully with a previous phone), so don't get mad if you've done everything and it's still not working.
But first make sure that the bluetooth adapter is properly installed. Check in Device Manager there are no yellow marks.
You need to configure the bluetooth services that you want to run on your computer. You may have been asked to do this when you first installed the software or the driver, but check again. If you have My Bluetooth Places on your computer, double click that and use the Bluetooth setup wizard to find out. Select I want to configure services. Then try File Transfer first, and follow the prompts.
Then activate Bluetooth on your Nokia. The first time you're supposed to give the phone a name and set visibility to ALL (you must have done that by now).
On the computer, My Bluetooth Places, double click Find Bluetooth Devices. If it finds your phone, you should be prompted to "pair" the computer with the phone, by giving your computer a name, entering a pin code (any combination of numbers will do) on the computer. Computer then should try to communicate with phone.
Here, if the bluetooth on the phone is working, the phone should tell you that another device is trying to connect, and ask you to enter the pin code. Enter the same code on the phone, and the computer should be added to the list of devices on your phone.
Then you can transfer files between the 2 devices from either end. To do it from the phone end, go to the application on the phone which has the relevant file, find the file, Options, Send, via Bluetooth.
From the computer end, double click the icon for your phone, and see whether you have an OBEX File Transfer folder. Double click it and you should see all the files available for transfer to the computer. Just copy and paste it to anywhere on the computer.
To send files from the computer to the phone, you can just right click any file (be careful it must be small), and click send to, Bluetooth, your phone name.
If it doesn't work, tell us which step is not working.