If you have no compression on one cylinder the engine will be significantly down on power as its only running on three cylinders,and it would sound dreadful.
The 1.4 VTi "BMW" engine has had lots of problems,including high oil consumption.The problem may be piston and rings that will mean a full engine strip down and rebuild. I would suggest you find a very trustworthy engine expert for advice.
Fitting a new engine will "correct the fault" for sure but will cost more than the car is worth.
That's basically what the mechanic I spoke to said old pug ,Igot codes 1336 +1337 on my cheap code reader if I remember right will need to phone the auto spark as I forgot to ask him for them but I remember it was showing a cooling system circuit fault.