Why is my car having trouble starting with a new battery?

Not sure what year your Corsa is, but I would think it does have a On Board Diagnostics. If you can, get it hooked up to an analyzer to see which codes it is giving you. That would definitely narrow it down. Disregarding engine size, the things to check are airflow sensor, crankshaft sensor, idle speed control valve and exhaust gas recirculation valve. Any of those can cause you considerable grief. Check the air filter and vacuum connections for any leaks and that they are on. Poor starting on those engines is often caused by idle speed control valve and most definitely the crankshaft sensor. As you can see there are numerous issues that could cause this. Of Course you also want to make sure that your fuel pump and fuel filter are working or replaced. You can download a Repair Manual for your vehicle from here. Hope this helps and clarifies it a bit. Good luck.

you should check for voltage drop on battery leads (measure at battery post not clamp) as I have had this in the job I do.