Hi, New to forum ( btw very nice walk throughs on web site)
My daughters boy friend just brought a 2002 F full fairing bike of eBay.
He passed his test yesterday so wanted a bike adap but this one had a few issues.

Now I rode it and seems ok while riding but if you pull up at lights or stop in Trafic it instantly cuts out unless you give it a hand full of throttle.
It then WILL NOT restart again no matter what unless you turn off the ignition wait 10 seconds and then restart.
It then idles perfectly, you ride away and it starts again. Soon as you stop the engine cuts out and have to do above to get it going again.

It also don't want to go faster than 85 mph but I think that is a diff problem.
The last owner replaced plugs, ht leads and finaly fitted new carbs and boots. None of the above made any change.

I haven't looked yet but I'm about to now. I do a little work on bikes but basic stuff. Service it and bearing changes but thats about my limit of knowledge.
I think the 85 top speed going by the huge vibes is the new carbs are WAY out of balance. This will be done soon as I get hold of a manual (i have a morgan carb tune) , intake boot seals seem to be a common problem when I searched so will check those though as carbs were replaced I'm thinking its not a carb issue.
The fact you need to turn ignition off for 10 seconds make me think cdi or tps maybe. Something electronic. But that's a wild guess.
Search came up with lots of useful stuff but 99% was carb or air leak based and didn't match my symptoms. So decided to jump in with a post.

Hope you guys can help

Oops my mistake, It's a 2004 FK4 GS 500 I have now been told   in black..... I'm sure the colour makes a diff

What is the odometer reading? Based on what you're describing, your valve clearances are suspect. Do a forum search for valve clearance and you'll find a whole bunch of reports similar to what you've described. Considering it's used, the valve clearances are something that you should check out sooner than later...and every ~4000 miles as part of regular maintenance.

And, pics are required for all mentions of new bikes. 

  big thx, spent a while searching and reading then decided valve clearence was most likely (as so much had been done by previous owner)
£80 quid later and droping 2 sizes on each shim he got the bike back from my local shop last week.

Such a difference, ticks over perfectly, revs cleanly and now go's a bit faster than 85

Btw as a side note, what a bloody silly place to put the left hand balance take off.
Wish I had pics but not my bike. Will try to get some soon though.