It had a mobiliser so we disconnected it then its not firing and the crank is slow what might be the problem

check its engine oil first......also check in morning there is any pollution.....if it have then replace its ring set and piston..

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Test the starter electrical circuit's . Main positive cable to starter , control side .Do you know how to use a DMM - digital multi-meter ?
No Crank Slow Crank

If it ISN'T cranking over ok ... and has a discharged battery..
Disconnect the leads from the rear of the alternator. A faulty alternator can discharge a battery within minutes. Charge the battery and leave the alternator disconnected. Try and start the car.

If - with a charged battery and alternator disconnected - the engine seems very slow to crank or makes a 'clicking' noise ... try cleaning the battery terminals - particularly where the black lead connects to the engine block/bodywork.

Check the leads -and terminals - for breakage/corrosion. A 'bad earth' or corroded/loose battery terminal can cause non-starting problems.

If all is ok and the car spins the engine but won't start, suspect a sensor fault.

Don't waste money on replacing part after part in the hope that the care will fire up. The best - and cheapest - option is to have an OBD - a hand held diagnostic check done. This will identify any error codes and tell you the cause .. i.e 'crankshaft sensor fault'.

CHECK BATTERY FOR CRANK POWER AND CONNECTION.

Tps has nothing to do with sparks. If you had sparks going to the distrubuter but none coming out, the cap or rotor is not installed correctly.

your crank sensor may be bad but if its turning over slow you may check the charge in your battery as well as your connections for corrosion

Slower cranking in cold weather is normal due to the oil being thicker and other tolerances being tighter. As long as the engine fires within 3-5 seconds I wouldn't worry about it. If it cranks REAL slow or is excessively slow to start, I'd tune it up (plugs, wires, distributor cap, etc.) and change the oil to the lowest viscosity recommended. Also, I'd have the battery tested and replaced if it shows marginal.

How about plugs wires.

When you say slow start do you mean it cranks slow of cranks along time before firing?