What your mate says makes every bit of sense, BUT like i say if the battery has got the guts to start the car again the alarm shouldnt have any problems, the alarm should even work right down at about 10.5-11 volts. They are extremely effecient. Its up to you if you want to try a new alternator/and or battery but its always annoying when you spend money and its not needed.

You'll probably have fun finding the earths, and also, by Thatcham spec there are 2 earths and they should have seperate earthing points Its hunting season!