1990 Toyota Corolla Could it be a alternator?

I presently own a corolla that has been handed down to me.
I recently have drove it and had no problems, but now. I am having issues.
It first started with the A/T oil temp gauge, the brake light on the panel, the battery light was lit, and the heater would not pump out heat as usual, all lights were dim, and the radio flickered.
I stopped. Turned the car off, and it restarted shortly with no gauges lit. However, the light's on the panel came back on, the same ones.
And eventually I lost all my lights, panel and all.

The car finally seems to have ran out of juice as I came to a hill and it sputtered with gas in it.

I am assuming that since it restarted it is not the starter. And that since the battery light came on with the A/T oil temp on (car was not running hot)
and I lost all power and lights, even my hazards seemed wacked. That it may be my alternator?

Please help me out, and let me know. I am limited on what I can do financially and looking for the most obvious reason for such problems.