electrical problem

I'm having a problem with my electrical system. About a week ago I installed a new battery, and a rebuilt alternator, the old battery was dead as well as the alternator. Now when I start the car up in the morning the battery indicator doesn't leave the red untill I drive for a few minutes, at which point the indicator goes up to regular levels. I'm not sure how serious this problem is as the battery does eventually come to the right level. Any ideas? Oh before you ask, no I haven't installed any new electronic devices in the car recently, no stereos, nothing. The last electronic device insalled was the alarm back in December, no problems until now.

Make sure to test BOTH battery cables. GM has had some problems with them. I already had mine replaced.