Definitely your battery has reached it's end-of-life.
Replace your battery.
Follow the appropriate guide on this website to do so.
The fan issue may simply be a secondary symptom of the bad battery combined with the reset operation that occurs when you perform that key sequence combined with the power button.
In my experience, the beeping is an indication of a problem with the RAM.
However, there could be reasons other than the RAM that could cause the beeping symptom.
Hopefully one of those other reasons would be an extremely bad battery, and nothing actually got fried when the battery died. (The fact that you can only get a reboot after performing the low-level reset that happens when you do that key combination combined with the power button, supports my thought that your battery is not just end-of-life… But died in a particularly bad way as well in terms of being able to boot off of AC power alone, without the assist of the reset operation.)
When your laptop is booted, you can see additional battery condition details by holding down the option key when you click on the battery icon in the menu bar. Most likely those additional details will simply confirm that you need to replace the battery.
Once you can boot normally after the battery replacement, avoid performing that particular reset except as a last resort to fix certain issues after ruling out all other causes.
Most likely you will never need to do that reset again.