Make sure your laptop is on a hard flat surface to allow for proper airflow and to avoid overheating issues. Another reason may be the fan on your device accumulating dust and debris over time, which causes the fan to not function properly. Use compressed air in small bursts about two inches away from the fan vents to clean them. If you have any further questions, here is a link to the troubleshooting guide for your device: HP TouchSmart 15-r015dx Troubleshooting
The first step for fixing a black screen is performing a hard reset. To do this, hold the power button down for a few seconds until your TouchSmart turns off. After a few seconds, hold the power button again to turn your device back on. If the black screen isn’t gone after the reset, the display screen may be faulty/broken. The only way to fix this is to replace the screen entirely. If you have any further questions, here is a link to the troubleshooting guide for your device: HP TouchSmart 15-r015dx Troubleshooting
The device's battery may enough of a charge to turn on, and function properly. The battery may not be fully charged. Try plugging the charger into the device to see if this was the case. If this was not the case, you may have a faulty battery. One way to check is to remove the battery, and then try to turn on your TouchSmart with the charger plugged in. If the device turns on without the battery, the battery is the cause. If you have any further questions, here is a link to the troubleshooting guide for your device: HP TouchSmart 15-r015dx Troubleshooting