Battery light stays on without ignition

[prusac]

First of all I would like to apologize if there's an already a thread about this one...

As the the tittle by itself says, my battery light stays ON without ignition. Goes out when I start the car and appears again when I turn the engine off. This cause my battery to be fully drained, since I didn't started a car for few days, although it's brand new. Got my battery fully charged last night and the problem appeared again this morning. The alternator has been repaired/restored recently, since the output voltage was somewhere around 12.5V.

It's a '99 1.4 Furio VTS, and ever since I bought it, it has been nothing but a really big pain in the ass with all gremlin electrical problems...

Thanks!