Finally! I finally figured out how to get my 3650 working as a GPRS modem! Some people had no problems and others were clueless as me, but I finally figured it out after playing with a bunch of options and both Bluetooth and infrared.
The first thing to do is make sure you have GPRS working. Normally on a Nokia 3650 you have three different Access Points, which you can find by going to Menu -> Tools -> Settings -> Connection -> Access Points. One Access Point is for MMS, the other for WAP, and the third is a generic GPRS connection to the Internet. The third is the important one. If you don't have the third Access Point, you need to call your operator because each telecom does it differently. Usually, it's just an Access Point Name like "p.movistar.es" and a generic username/password like "MOVISTAR" with no gateway settings or anything like that. Make sure that third connection point is working by grabbing an application that uses the Internet directly, like the Doris web browser or Wireless IRC, and test that connection.
The second thing you need is the *key* and this is the part I didn't have until just now. You need to specify the Access Point Name of the generic internet connection for your phone to know how to connect when its being used as a modem. You put that here: Menu -> Tools -> Settings -> Connection -> GPRS -> Access Point. Mine looks like this: "movistar.es".
Now in case you're confused, let me go over what I did and why. First I didn't understand what needed to go in that field or even why it was used. It's sort of off by itself. But after some playing I realized that it wasn't the name of the Access Point itself, but the name of the internet Access Point Name listed inside the AP options. But with Movistar, normally I have to use an address that starts with "p" for "prepago" (prepay), but I know from months ago when I was first having problems with GPRS when I first got my Nokia 7650, that Movistar normally uses just "movistar.es". So when I popped that it, it finally started working.
Okay - here's the rest of the instructions. If you don't have Bluetooth, then you can use your phone as a modem via infrared really easily. Go to Menu -> Connect. -> Modem -> Connect via Infrared and your phone will turn on the infrared port and be ready to used as a modem. If you're using Win2K or WinXP, the OS will detect that the phone is there and communicating (if your infrared port is working) and install the phone as a modem. Then you just add a new Dial Up Internet connection as normal (via the connection wizard), but instead of using your normal modem, you use the IrDA modem. Leave the username and password blank (I put in MOVISTAR/movistar just in case, but I don't think you need it) and in the phone number use *99#. You computer should then connect to the phone and to GPRS.
If you're using Bluetooth - it's a bit weirder, but generally the same. Basically, after you've installed the Bluetooth drivers, you should be able to go through a Wizard to set up a Bluetooth modem. Once you've struggled with all those options, you add a new Dial Up Connection like above, and use the Bluetooth Modem, with the same number to dial.
Works like a charm! And it's *a lot* faster than the modem... makes sense, but when you see it with your own eyes, it's pretty cool.