When the power button is pressed the computer beeps repeatedly and does not turn on.

There are a few things you can try. Some of them are addressed in the trouble shooting page linked here HP Envy TouchSmart 15 Troubleshooting . You can find some of the answers under the section Computer does not power on.

The battery after many charge and discharge cycles will lose it's ability to hold a charge. Extreme changes in temperature can also reduce battery life, as well as keeping it plugged in all the time. You should let the battery completely discharge once and a while to help it have a longer life. If the battery is unusable for your needs, you should replace it.