Peugeot 306 Gti wont start?

I have been having problems starting my 306 GTI-6.

It had been left alone for a few months. When I came back to it the battery was dead. I charged the battery up but it did seem to have enough power to start it. (all the lights came on and the alarm went off but only barely turned over)

Have tried jump starting it but with the same outcome - (turns over a couple of times but never enough to start it)

So I bought a new battery and put that in, Lots of battery power, all the lights were bright but when I went to turn the ignition to start, everything cut out (lights, dials everything went out - not even an attempt at turn over)

The new battery is the same as the old one (075) but new one has higher Cold cracking amps (cca 600) vs cca 475 on the old batter, both 60mA.

Any help is great appreciated?