Firstly as MarkGSi said, check the battery terminals are secure, if in doubt, clean the clamps with wd40, sand it down with very fine paper to new metal, also clean the battery stumps. Re-attach, spray with wd40, then put some petroleum jelly to avoid corrosion and protection. Check all all other engine bay earth connectors too, there is one under the battery tray.
But I'm with Jowley on this one, dying batteries can play with your mind, they seem to work one time, and the next time they will struggle, and then nothing, and then it may work again after that, etc. All this is because of a dying cell within the battery causing havoc inside the battery. As you may know, there are 6 cells all giving 2.1volts in a car battery, connected up with a small loss giving you 12.6v, a dying plate will break up the connections to the other plates hence the weird activity of a faulty battery.
Obviously, if it ISN'T a maintenance free battery be sure to check the water (de-ionized water), if it's low, top it up and give it a good charge overnight.
These cold spells we are getting can affect seemingly good batteries quickly not only because the low temps are not good for the cells and chemical reactions within the battery but also because you will tend to use more anciliries... light, demister, fan, radio louder cos of fan, etc.
A load test on the battery by an auto electrician will confirm things before he sells one to you anyway.
