From a stand still if you accelerate hard vehicle starts vibra

could be a engine mount, any engine setting out of line will add more load to the engine mount movement, air leak in manifold, bad spark. it could als be something as simple as a thrown wheel balance or the balance on drive shaft balancer is out of sync, or missing.

Yes indeed.

You want to get the vehicle drive shaft (torque tube) checked for any loose end play... paying particular attention to the "U-joint" area.

As bad as you are describing it it sounds like you are really close to dropping your drive shaft...

DO NOT work on this yourself if you are not TOTALLY familiar with good jacks... jack stands... wheel chocks and have a level work area available... also keep in mind that while your TRUCK may be in PARK... that is only as stable as your drive-shaft.

Don't get between your truck and a hard place until you get that DRIVE-SHAFT fixed...

Another hot tip... if you are going to the trouble of removing the drive shaft... replacing both "U-joints" would save money and time in the long run.

Be safe... work safe!

http://www.rangerforum.com/threads/u-joint-replacement.6756/

UN-Edited response via comment line:
Oh yes indeed.

It appears that the Ranger can come in many different configurations... but the rules of home trouble shooting are to go after the cheap and obvious probabilities FIRST, (loose lug nuts) then on to the rear-end... CV-joints (if you have them)... wheel bearings... finally back up into the transmission.

Seriously... look that drive-shaft over:

Have an assistant hold one wheel while you move your rear wheel... while you are watching the drive-line... the offending u-joint should reveal itself by showing some free-play.

These should be very tight...

Perhaps then when you look more closely you will see the HORRIBLE (chocolate) brown color of oxidized iron... ALWAYS an imminent sign of DANGER anywhere on your vehicle.

The u-joints can be pretty bad... and the vehicle still run... but once that drive-shaft drops your parts costs will escalate vigorously (assuming everybody survives (my drive-shaft didn't... but mine did NOT warn me (silent failure)).

Please do have a look at the URL I posted with my first reply.

Be safe!

that could be transmission issue/ front end issue/ with out driving the vehicle hard to say.
my 88 had overdrive shudder going up hill transmission need a rebuild. that all i got with out driving the veh srry.
when trying to figure out what going on with the veh you need to isolate the cause of the vibration , front. rear of the veh.put the veh on jack stand and drive it see if you can figure were that vibration is comeing from

Chances are its a minor miss in one of the cylinders. You don't feel it neutral at idle or until the trans goes into overdrive because those times the engine is not working very hard.
If it is a miss fire the check engine light will come on when it gets bad enough to affect fuel mileage.
If you have not yet changed the plugs I would start with that. There is also a chance you damaged the engine when it overheated.

Its possible that the drive shaft has something on it causing this vibration for example I accidentally sprayed under coating on part of my drive shaft and the vehicle did exactly what you describe until I got it scraped off. Additionally if its cold where you are ice can freeze on one side and cause this issue as well.

Download this link and find your Service manual for your vehicle. It will serve you well and to keep for future reference

http://ezinearticles.com/?Find-the-Free-Auto-Repair-Manual-You-Need-Online&id=92717

if it is not missing then the problem is most likely engine mounts that have gotten hard from heat, this is the common reason and the 1st thing we look at if the engine is running ok and not the source of the chassis vibration.

Increased vibration from a vehicle indicates worn out engine supports. This vibration often disappears when revving the engine high, but is very noticeable at low revs.

You can have these inspected and possibly replaced to reduce the vibration cominf from your engine.

Hope this helps.

I would venture to say your exhaust is hitting your frame, or, you may need new motor mounts. The exhaust is what I would lean toward. If you can imagine your exhaust sitting under your vehicle, and the fact that the vehicle has a little age, the motor mounts probably give a little, causing the motor to move slightly on acceleration and deceleration, thus your exhaust is going to move, and may be vibrating on whatever its touching. Good luck.

This may be caused by bad motor mounts. Lift your hood and then start the engine. Put it in reverse and hold the brake. Push on the gas peddle and watch the engine. If it trys to roll over they may be bad. Be careful.