Firstly, you don't say if its petrol or diesel?
Assuming its petrol;
Being a 2000 model its most likely fuel injected so when starting there is no need to touch the accelerator as everything (air/fuel mix) is controlled my the engine management system - unlike older cars with a choke & carburettor.
Fault tracing between battery, alternator and coil packs isn't easy and requires diagnostic equipment. If there is more than one problem that skews the results it becomes double difficult.
Based on it having an engine management computer - your best (and easiest) option is to get it connected to a computer and have the error codes read - the computer logs all sorts of parameters and details of components it suspects are failing or likely to fail. A good honest small independant local garage might do this for you for free. If not, negotiate a fixed fee - I'd say don't think of paying more that £15-£20 as all they are doing is connecting a computer to your car and printing the errors - 5-15 minute job. Once you have the error codes it should give you an indicator of the problem.
If as you say the car won't start unless you press the accelerator - perhaps one of you sensors (airflow) is faulty/broken.
With regards to your battery - how old is it? did it play up last winter? Is it topped up? (if not a maintenance free type). It is possible for a battery to regain some charge, overnight for example, to give enough power to crank the engine once. But a failing battery can instantly be killed by the cold weather.
Also have you checked the battery terminals and connections? Corrosion on the connections can cause some erratic problems like a flat battery that works as normal after a short period of time.
You can't test your alternator until the engine is running and it isn't involving in starting the engine.
EDIT: If you have a home start breakdown policy then you may be covered for them coming out and reading your error codes. Or if you are away from home and it won't start, call them out and suggest they read the codes and get you started :)