I'm sorry but if the starter does not even click when the key is turned, a set of plugs isn't going to fix it. I think it's time for a new family "mechanic". Maybe time to trade in for a technician?
It sounds like just a bad starter. The whole oil change thing was most likely just a coincedence.
Word, I was going to say the same thing, but I didnt want to waste my typing to someone who doesnt take our advice...First he said his car cranks over but doesnt start and now the starter doesnt make any noise. It's probably more than one problem.
To the OP, spark plugs are probably the least common thing to go wrong with your car. Unless your burning an ungodly amount of oil and fouled the plugs. They last well over 100,000 miles. They don't have a characteristic of just not working one day. You will notice it go bad over time if you had bad plugs. Your car would have probably popped a CEL in your face for a misfire because one or more of your plugs isnt igniting the fuel. A Car will keep running even if one or more of the plugs are bad BTW....
Check your CLUTCH RELAY in your fuse box to see if its working. If it is broken, it wont even allow your car to turn over at all, not even a click. You need to check that first. It its working properly then do this,
If your starter is not turning the engine over, u need to lightly tap it with a hammer. If the car starts to crank but wont start, then spray some starting fluid into the intake throttle body.
You need to go to the root of the problem before you just start buying parts for your car, that's how you save money.