1991 Plymouth Acclaim ignition

Sounds like you may have a bad ignition switch.

The ignition switch is a common item, but you also have to look at the terminals are wires. If two terminals are blackened and overheated, the plastic connector body will be melted too. You'll need to replace about 4" of those two wires because they'll be hardened and solder won't adhere. Be sure to seal the connections with heat-shrink tubing. Never use electrical tape because it will unravel into a gooey mess on a hot day. You can cut the terminals out and install two crimp-on terminals, but solder them too, then plug them in individually where you cut the plastic away.

If you don't replace blackened terminals, they are going to create a high-resistance connection. Those will develop heat which will migrate into the new switch and cause the same problem you have now.