Typically if the motor is good and its not coming on, the switch is worn out or somehow disconnected. Also make sure there is a good ground (-) connection.
Assuming there are no speeds at all, check the switch and electrical plug to the switch for a melt down situation.
fuse, wiring, blower motor, blower motor switch, blower motor resistor
Could be, a blown fuse, a bad blower motor, a burned out blower motor speed resistor, a bad blower motor switch,
the windings inside the blower motor can be shorted out fan will work but takes too much power could be a schafed wire as well or the blower motor could be seizing up..
You don't say the reason for the blower motor replacement. Did it not blow ? If that be the case, and you do have a new blower, check for 12 volts to blower. Could also Abe a malfunctioning blower module. Now if its blowing COLD air, well , replacing the blower moter wont make it blow warm. There could be numerous causes of that problem
Check to see if you are getting power to blower motor - if so replace blower motor If not check fuse, switch, resistor pack.
Check your blower motor relay!
could be the resistor on blower motor is bad
The 1998 Dodge Neon does not have a relay. It does have a blower motor resistor that could be bad.
Loose connection or blower motor is bad
Check all the fuses and relays first. If they all appear to be in good working order, then you'll have to get to the blower motor. Could be a short or the motor could be bad.
Could be, Blown fuse, Bad blower motor, Bad blower motor speed resistor, Bad blower switch,
can be the heater blower motor resistor located in either the ductwork or under hood near blower motor on firewall