2004 Honda Accord Alternator?

I have a 2004 Honda Accord Coupe with 90,000 miles on it. Over the past two months, my car would not start on random occasions. Eventually, I had to step on the gas pedal for my car to rev up and start. I took my car to Midas and they did an electrical test. They said the starter was fine but the battery would need to be replaced. Therefore, I replaced my battery two weeks ago thinking that this would solve the problem. However, my car continued to have problems starting and now seems to have given out completely. The car sounds like it is definitely trying to start; however, it dies out and fails to do so.

I have been told that the problem may be the alternator. Could this be the case and how much will it be to replace it?

Thank you, I appreciate your help!