There is one other thing that will prevent your battery from giving full power for starting the car, it is caused by corrosion of the positive (+) post connection to the cable clamp. It never happens to the negative terminal. It shows as a white fungus or blackening on the post and clamp and if you start the car and immediately put you hand onto the positive battery connection it may feel warm or even hot. You will have to take the clamp off and clean the terminal and connector with either wire wool or that green nylon scourer stuff. Put vaseline on the connection and bolt it up firmly (the vaseline seals the connection to stop it corroding again - ONLY USE VASELINE OR PROPER ELECTRICAL TERMINAL GREASE, DO NOT USE NORMAL CAR GREASE BECAUSE IT WILL INSULATE THE CONNECTION ). It is also wise to check the connections of all heavy cables to battery, bodywork and engine as these can also cause 'voltage drop' in the starter circuit if they are not clean and tight - vaseline on those will be a good idea as well.
A problem with a bad battery or connection can be highlighted if you switch on your headlights and get someone to watch them as you start the car, they should go dimmer, but not completely dim out (the system voltage drops to 7 to 8 volts on starting in colder weather). Also, with the engine running at about 2000rpm check the battery voltage with a meter, it should by around 13.8 to 14.5 volts, if it is below 13.5 it may be alternator problem and will not reliably charge your battery. After a run in the car, leave the battery to stand for about an hour and then check voltage on terminals - a healthy battery should settle to about 12.5 volts, if it is less than 12 it shows battery is on the way out.
An interesting fact for anyone who had a car before about 1980 is that before that date you used to get cars with either the negative or positive side of the battery earthed to the car body, and radios had a switch to select for + or - connection. Now cars are universally negative earth and the reason why they were changed was that positive earthed cars suffered from bodywork corrosion much more than negative earthed. That may explain why a lot of British cars used to rust away before your eyes.