Chrysler Repair: perplexing problem with 97 LHS chrysler, fuel pump relay, battery cables

Question
After a snow storm and not starting my car for three days, it would not start or crank..just a click.. so i asked a friend for a boost and before they tried to boost it they cleaned off the very corroded cables..cut back the battery wires and put on new terminals. it still would not start so i called AAA for a boost and they started it and said the battery was shot.. i drove it for an hr or so and then went home with the intention of driving it to store the next day to replace the battery. it would not start next day even after 3 different AAA calls for help.got a ride to buy a new battery and had it put it in and it still would not start but cranks over good.  left the car to sit for a few days, then it started right up..drove it for 5 days or so no problems. another day went out and the same problem started again..it would only crank good but not start. it appears the fuel pump is not coming on during the times it will not start, but works good sometimes.  cked the fuel pump relay..it was ok, it does need a tuneup, but gets a spark, oh..also friend changed spark plugs but not wires. was told by dealer it has a bad wire leading to the fuel pump but they said they can't tell me if the fuel pump is any good until the wire is fixed. and Firestone said it needed a fuel pump, but went I went to get it..it started right up and drove for days. don't know if i should fix the wires..the dealer did not do a test for the trouble codes for some dumb reason..they just said i should get a new car, but the car has always started with no problem until my friend cleaned off the battery cables and replaced the terminals.  it has 144,000 miles but mostly highway, and has been good to me for the 6 years I've had it.  I need to keep it at least another 6-8 months till i finish school and relocate.  Please tell me any info you think.  thanks..sorry i have no real car tech experience. but plan to have another mechanic look at it...not a rip off shop though.

Answer
Hi Belinda,
One way to access the fuel pump is to listen for its hum when you turn the ignition switch to the 'run' position before you then go further with the key to the 'start' position. It should hum for 1 second or so, normally. It will hum again in the start position, ideally, but it is hard to hear it over the noise of the starter motor. It is possible that the ignition switch is flaky. You could check fuse #14 behind the dash (remove left end cap of dash to access) to see that it shows 12V when the switch is trying the starter motor function which would be a test of the switch.
Getting the fault codes would be a good idea. So the next time you get it going you can go to the mechanic you trust or to an Autozone parts store for a free readout of the codes. Then ask for the 4-digit fault code numbers and get back to me with those for further evaluation. Because the issue began with the battery cables, you might want to look again to make sure that all the wires are tightly connected to the clamps and the clamps are on the battery, and as well that the wires that are attached to the -clamp are firmly attached to the points where they routed to assure good ground current return paths to the battery. If you use a wrench on the + post clamp be sure to first remove the - post clamp from the battery first as a safety precaution against an accidental short to ground which would cause an arc and possible personal burn in the wrench happened to come in contact with a piece of metal while you were applying to the + post.
Roland