Hi SMattson, if your problem is with a 3-prong cord to a 3-prong receptical then the fix is fairly easy, just go to the local hardware store and buy a replacement cord which matches the pattern of the receptical (i.e., blade, blade, "L"shaped blade), just make yourself a diagram of the pattern. However, if the problem is with 3-prong versus 4-prong, you'll have to wait for someone else to answer your question, sorry to say but I haven't had any experience with the new 4-prong's. Anyway, good luck and I hope this helps!

for years electric dryers and ranges were allowed to be a 3-prong deal.
This meant that @ 240volts there was Hot-Hot-Ground.

The problem was that ranges and dryers began evolving many 120vac assessories, lights, timers, bells, whistles , etc....

This meant current was 'returning' on the grounding conductor. Granted, a negligible qantity at first, but increasingly so, thus this introducing a hazard.

So it became a code ( i'm thinking the 93' or 96' cycle without looking) to have a 4-prong receptacle and 'pigtail'
( cord from unit).

so now we have Hot-Hot-Nuetral-Ground

This is not so far fetched if one considers the modern day receptacle that has Hot-Nuetral-Ground ( looks like a face with the ground down)

On the newer Dryers there is a bonding jumper that must be removed in order to isolate the Neutral and to properly install the Equipment Grounding(Bonding) conductor.
There is a real hazard with the Three (3) conductor cord-sets by using the Neutral for both the neutral and the equipment grounding conducor. Especially since the motor is 120 volts, if by chance you lose the neutral, albeit loose, broken or if it comes apart, the whole appliance will be energised and can become a serious shock hazard.
Be careful and be safe.
Mark