1998 Honda Accord Car will not hold charge

Hi, my 98 Honda Accord LX with 160,000 miles on it quit running the other day. I was driving about 40 mph and every time I would step on the brakes, all the lights on my dashboard (ie. car door open, engine light, oil light) would come on but then as soon as I let off the brakes they would fade out. After about 20 min of this, my radio would short in and out. Then I pulled over and turned off my car, when I tried to turn it back on it would not start(like it was dead). I left my car there(I had to go to work) for about 9 hours. When I returned back to my car, it started(without a jump). So I drove it for about 15 minutes going 45 mph and the radio, lights were still fading in and out and this time the the speedometer and rmp needles was dropping from 0 to 45 while I was driving. They finally dropped to 0 and would not move. Then after about 5 min the car died and would not turn over. I tried to jump it but the battery will not hold a charge. I cleaned off the corrosion on the battery, but still nothing. It starts but quickly dies after. Could this be the alternator?