Easy there, friend. Keep your cool.
It would be good to make some voltage measurements with the car running.
Also note whether the red/orange battery light (or alt. light) in the instrument cluster is lit.

My '86 (R.I.P.) had a rotten wire harness going down from the alternator, curling under the timing belt cover. The small + wire broke several inches before it reached the alternator terminal. I patched it back together several times. Ultimately someone (not me!!) dropped the alternator with wires still attached, after that it never was right again, even though they replaced the alternator and battery immediately following the drop. I'm convinced that spending the time to open up that wire harness and rebuild it would have kept the electrical system going as designed.

I'd stay away from Autozone as far as Volvo parts is concerned. I do like fcpgroton. They are brick specialists.
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Sven: '89 245, IPD sways, electric rad. fan conversion, e-codes, 28+ mpg - auto tranny. 850 mi/week commute. '89 245 #2 (wifemobile). '90 244 (spare, runs).