Need help getting the wires re-connected that go to heater element and run the fan on this space heater that looks like a mini-electric fireplace.

What fan ? radiator cooling fan or the heater blower motor . Looking at wiring diagrams for the affected fan , to see what controls it . . Testing the electrical circuit's ,this is how to diagnose ! Could have a relay with stuck closed contacts , a bad control module ,control wire shorted to ground etc.... Free wiring diagrams here http://www.bbbind.com/free_tsb.html .
Learning how to test automotive electrical circuit's would be a good idea too .
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A fan heater is a fan blowing over a bank of electrical elements, or in many cars, hot coolant water is directed through pipes in the heater assembly, in place of electric elements.
In any case, if fan is still running when heater is turned off, the source of the heat will be gone, so blowing only cold air.

You just have to look at a new motor online to see that it has only two pins in the connector. Removal is another story. I have pasted the procedure from Autozone.com below.

Removal & Installation

Before servicing the vehicle, refer to the precautions section.
Disconnect the negative battery cable.
Drain the cooling system.
Discharge and recover the A/C refrigerant.
Remove the instrument panel by removing or disconnecting the following:

Battery box
Intake filter housing
Heater hoses
A/C pipe from firewall fittings (plug openings)
Heater locating stud nut
Steering column from steering gear
Steering column from rubber bellows
Left and right A-pillar trim
Radio
Cover from beneath center controls
Left and right kick panels
Connector behind left kick panel
Upper connector from blower control
Instrument panel end covers
Bolts behind end covers
Lower section of steering column trim panel
Electrical harness from instrument panel trim
Connectors on steering column
Heater connector
Lower bolts on instrument panel support (next to steering column lower end)
Instrument panel

.Disconnect the fan motor wiring harness.
Remove the fan motor.

To install:

Install the fan motor and connect the wiring harness.
Install the instrument panel in reverse of the removal procedure.
Refill the cooling system.
Reconnect the negative battery cable.
Evacuate and recharge the A/C system.
Check the coolant level after starting the engine and running for several minutes.

There is a good chance that the wire harness to your heater blower fan resistor is damaged from the heat generated from the current flow. Inspect the wire harness at the clip, which is the most common area of where the issues needs to be addressed.

The plastic clips melt and then covers the electrical terminals causing poor connection. The lost of connection will give you the issues you have described and the other area would be the switch is self. A spry of electrical contact cleaner will fix a dirty switch.

Thank you for using fixya and good luck

The inoperative cooling fan needs to be diagnosed,run the engine until it reaches 229degrees and seeif the fan gets power to turn on if so then replace the fan if not check the wiring and cooling fan relay and repair or replace as needed.

I assume this is a 240 volt water heater that runs on a 30 amp circuit. Read the instructions that came with the new water heater to be sure. If the wires are connected correctly then you have a defective water heater. Let's first make sure it is wired correctly. Turn the breaker off and take a look at it. It must be a 30 Amp breaker and the wires going to the water heater must be 10/2 with ground. This is an orange wire. If you cannot see the water heater from the service panel it must be wired to a disconnect box. Look at the breaker and make sure the red & black wires are tightly connected to the double pole breaker and the copper wire is connected to the ground bar. At the disconnect box (if applicable) the red/black wires from the service panel must be connect to LINE and ground to ground bar. The wire going to the water heater from the disconnect box is connected to LOAD. It is easy to get these mixed up because they are not always in the same location and are hard to read on some disconnect boxes. Look carefully and make sure they are correct. At the water heater you connect Black to Black and Red to Red. Make sure the ground is connected tightly and none of the wires are touching each other. Use wire nuts and then tape the connections with electrical tape. You should not have applied power to the water heater until it was full of water. If you did then your burnt out the electrodes. I would suspect you have a short somewhere or the water heater is defective.

ok there is a sensor the one control the fans but you can find a load information just go to autozone.com and aalso you can find the location of the sensor too

Hi: Sounds like a possible heater resistor problem. First check to see if heater fan working, unplug heater under hood and put 12 volts to it from the battery with a wire (single black wire running to back of fan). If works then problem probably the resistor which is located on the fan housing under the hood to the right of the fan. The resistor has wires to it running from the heater fan, 2 - 7mm screws holding resistor in place, check resistor to see if any of the 3 elements are melted off, if so replace. Note: Rear window defrost has nothing to do with heater fan. Hope this helps...

its more than likely the earth wires for the lights. unplug the lights and chec the connections visually for corrosion or burnt. the white wire on either side is the earth. get some electrical cleaner and spray the connections. should solve it

A friend here solved it. It was a bad connection of the ground wire, with the paddle-shaped connector loose. He cleaned it a bit, slid it back on, and crimped it a little (not easy to do in that tight space). Solved both problems.