Rough to stalling idle

run scanner to pinpoint problem check for vacuum leaks

Make sure it's charging ok.
Jump starting can cause trouble.
If you don't have a way to check the voltage ,put jumper cables
on it and see if it runs better.

I had to change my stator

Check the IAC valve...or sometimes known as an electronic choke. That valve is how your engine gets air when the throttle body plate is closed. If the valve is stuck due to malfunction or carbon build up then it will cause that problem, and give you a rough idle at best.

You need to completely drain and refill the gas - the gas you have is stale and doesn't have enough power to run the bike.
The battery needs to be fully charged - not just jump started. It wouldn't hurt to do an oil and filter change as well as a air filter and plug change.

I am not sure though, but just check the bike's manual for a FUSE. It is because I too had a bike but not a good one and I had some what similar issues. I found that the Fuse in the bike has gone. If the fuse has gone bad then the bike will not run So try changing the Fuse. If you have any more questions you can have a look at the link below.http://images.google.com/imgres?imgurl=http://faq.f650.com/GSFAQs/Photos/FuelInjectorPhotos/ThrottleCableAdjust.jpg&imgrefurl=http://faq.f650.com/GSFAQs/custom_fixes_for_s_and_s.htm&usg=__iPXXYSkvsJBDslHiFDaPQm1SMUY=&h=600&w=800&sz=54&hl=en&start=13&um=1&tbnid=nbW6uz0JKRUyEM:&tbnh=107&tbnw=143&prev=/images%3Fq%3D2003%2BF650%2Bdakar%2Bbike%2Bbattery%2Bcircuit%26hl%3Den%26um%3D1They have discussed the topic in bottom of the page. Kindly go through the same.Good Luck !!!

has anyone checked for a vacum leak? a vacum leak will cause rough idle at idle. check the lines from the pcv valve.

Check the voltage of battery with voltmeter.. It is sometimes possible that if voltage of battery drops and jump start is needed, your computer will only charge to the last voltage that was recognized which would be when jumped...Try and charge the battery if possible I would actually suggest that you have your battery tested at local auto parts store and if it is presumed in good condition ,let them charge for you to max capacity . If battery has been tested and labeled as no good replace if necessary... Oh, and first thing you should do is make sure your positive and negative battery connections are clean and tight...if this didnt fix problem please give more info on what was found when advice above was followed...Good Luck!!!!

First thing that came to my mind is the AIC Valve, If it's not that, you may want to check out the idle control system (I forget what it's called.... I can check if you want.) It's attached to the throttle bodies on the right hand side and it's basically a set of motors (maybe part of the choke system) My bike is throwing a code for it, and it will die every once in a while (still can't ride it, but at idle) And if I hold the throttle open at all, it'll be fine