Sounds like the synchromesh rings/cones have disintegrated. The same could happen to the others - not just between 2nd and 3rd. This could be due to ingress of water in to the gearbox (if it was second hand, it could have been lying exposed in a scrapyard before it was fitted in your truck).
Although you could try taking off in 1st (you'd normally take off in 2nd unless the truck is fully laden) and skip to 3rd etc etc, it isn't the kind of thing you should be trying to live with. The economics of whether you should scrap it or not really depend on your financial circumstances and also what type of body and or special equipment (if any) is mounted on the chassis and the general condition of the engine and the rest of the truck.
You could get the gearbox overhauled.
JD
May 2008