Can old batteries at full charge effect reception?

I currently have a 6310i, which works ok, but I don't get reception in my apartment. I will also get messages that someone called hours after they called (I even broke up with a girl when I thought she was ditching me, just to find out she tried to call me several times, ouch).

I'm currently on the GSM network with cingular, ported from AT&T.

Anyway, my battery is a li-polymer 1200mAH BS2. I've read that the li-polymer batteries don't have any mempry-effect on their charge, but I can only guess that the reason I'm having these problems is due to 3 reasons:

1. Battery is getting old & it doesn't have enough power to pickup signals.
2. Internal antenna on the 6310i is bad (but I've read no one had problems with it before, so......)
3. The Cingular network in my area sucks.

Can an old battery effect a phones reception? All thoughts are welcome.

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I'd say no. The battery does not really effect the reception, the tower puts out a signal and it either reaches the phone sufficiently or not. If it reaches the phone with enough strength, then if the battery is weak it may not amplify the signal enough, but I'd only expect that with a nearly dead battery, if then. I'd say the battery would die before that became an issue. The next option would be the phone itself (antennae) is possibly bad or is an out of box failure.

maybe the walls or something blocks the signal?

Is this a new problem? If the signal has been this bad all along then that is probably what you are stuck with for cingular coverage.