You could have a blown fuse, bad relay, bad blower motor resistor pack, or just a bad blower motor. Start with checking your fuse to make sure you have power to you blower motor.
Is the oil pouring on the ground as you add oil? If yes, the oil drain plug could be missing, or installed loosely; the oil pan could be damaged, the oil pan gasket could be broken or missing, the oil dipstick pipe could be loose where it meets the engine. Are you a first time car owner? Have you overfilled the engine with oil perhaps?
Hooking up a scan tool to see if the engine computer is communicating should be done . The ECU - engine computer controls a relay to energize the fuel pump relay . Do you know how to do automotive electrical testing using a DVOM - digital volt ohm meter ? How to read an use a wiring diagram to find testing points in a electrical circuit ? It's probably the main relay , this powers up the Powers up the ECU ,that's why the check engine light is not on .
For Michael Subaru Main Fuel Pump Relay check out
removing a battery terminal can often corrupt the CPU program in the ECM
first try using the scan tool to reset the ECM
check for cam sensor wires /loose connections from moving the harness around to remove the plugs
you can purhcase a replacement remote and program it to the car. http://www.cars101.com/subaru/keyless.html
that link will give you instructions on how to add a new remote
Have you had it hooked up to a scan tool ? check sensor data ! Your vehicle has no cold start valve . Black smoke out the back indicates a rich condition , holding gas pedal to the floor causes the engine computer to go into WOT mode shutting off the injectors . Suggest you do injector leak down test , leaking fuel injectors ! Ever replace fuel injectors ?
The M8 bolt that secures it is easy to remove, but the sensor is often rusted in, especially on the rear. If so, you will have to remove the rotor and hub. The ABS sensor coils region is about 13mm diameter, the sensor magnet tip is about 6mm. Find a LONG 1/4" shaft socket with outside dimensions a bit less than 13mm. This will fit over the magnet tip. The base of the socket sits on the coil. GENTLY tap the socket, and if you are lucky, the ABS sensor will slide out without destroying itself. Be prepared to replace the expensive sensors if you damage them. Parts suppliers are much cheaper than dealers.
It almost sounds as if you had some sort of security system in the car that disables the ignition and prevents the car from starting. How do you know that you have power to the starter? Does the engine actually turn over? If that is the case, you might have a bad wire connection from the starter to the main power supply.
If your car has a cable speedometer it needs to be removed from the transmission to install it on the cluster first. Lift up the rubber boot that covers the end attached to the transmission. Now find and remove the retainer clip, take a pic or sketch how it looks installed before removal. Some versions of the cable use a hex threaded end and will unscrew with a wrench.Now you can pull the cable out of the transmission do no use excessive force it will just pop out. With the slack you can now easily attach the cluster and the electrical plugs.