Car problem

I have a very old car and it finally started to give me problems that I can't ignore (i.e. not starting any more).

Last Friday when I try to start the car, it won't start. The day before I noticed that when I try to start the car, the starting process sounds "slow", but didn't pay attention.

Now the car won't start, I started to dig problems.

My first thought is the battery, but I want to make sure there is no other problems. So I jump up the car, and checked to make sure the alternator is producing electricity. Then I checked for leaks. I am a total amateur on this, what I did is, disconnect the battery, and measure the resistance of the 2 wires. The resistance is 0!! After some search, I understand that there are diodes inside the alternator, and I should measure it positive to positive. Still it is only 20 Oms. So I started to suspect that my alternator diode is bad. A friend of mine also had the same car type, and I measured his resistance, also 20 OM.

So based on that, I am pretty sure it is my battery. Changed the battery, tried to start, and somehow my security system won't let me start! Guess it is a all new round to check my 10 year old security system (which is installed before I bought the car).