Ford Focus Mk1 1.4 Starting/running issues

Hi everyone,

First of all thanks for having me.

Recently a mate came to my house on his FORD FOCUS CL 1.4 ZETEC 2003 and after couldnt start the car, battery gone dead so the car was parked up for a week. i brought the car of him cheap for a fix up and sell one.
charged the battery and would start and die. checking under the bonnet i found the pvc hose with tape around it. ( lovely fix from previous owner ) brought new one fitted and still the same.
Done a quick look up online and they known to ***** the coil so as wasnt too expensive got it and with new plugs.
Removing the old plugs they had quite bit oil on the wells.
Removed the valve cover and fitted new seal around and fixed the oil on the spark plugs
after fitting all back i started the car and the car idle and giving bit gas, smoking quite bit and then smoke ( white ) gone away.
couple days later i gone to start the car again and it would stall on idle.
I hear the buzzing for secs when i turn key.
as you can see on the video it starts and kind runs then dies.
I have cleaned the throttle body, idle control part.
I have unplugged the fuel line at engine bay and huge spash of fuel as u would expect but not having the right tool to measure the presure its hard to figure out.
Also i have a question would a bad battery make this cause?
This model does not have the MAF SENSOR at all near the airbox.
This car is in very good condition for its age with 130k on clock with service up to 100k.
Fuel filter seems new
Mate told me could be.

fuel pump
crank sensor
blocked injectors

Please i am looking for honest help had people telling me to scrap but i would feel so bad throwing this car in this conditon away to the scrap.
 

video http://sendvid.com/aj5o8g7d