Most likely you have a hardware issue with the laptop since the fan is running at high speed and you have a charging issue. Most likely the issue is with a bad battery or a bad Logic Board. The fan running at high speed indicates a temperature sensor is not being recognized...my guess is the sensor for the battery since you are also unable to charge the battery.
You can also try booting into Safe Mode in case you have an issue with some third party software which is causing the laptop to run hotter. If Safe Mode allows the fan to run at slower speeds, then you can look for possible software issues by running EtreCheck and posting the report here using the "Additional Text" icon which looks like a piece of paper.
If you can boot the laptop normally or into Safe Mode, then check the battery's condition by Option-clicking on the battery icon on the menubar. If the condition is listed as "Service Recommended", then you will need to have the battery replaced.
If none of the suggestions posted here help, then I think you will need to have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate.