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Welcome to JA.
Try jumping it and then turn the steering wheel lock to lock and see if the HDC light goes out. If not you will have to have the fualt codes in the system checked to see what is causing the light to come on. For the check engine light you will also have to have the codes checked because it could be a lot of different things. It may just be related to low battery voltage and could just be cleared out.
HDC is hill descent control
Check engine light means a malfunction in the engine management system.
No if the a fuse is blown for the pump the pump would not come on. These pumps can be a little difficult to install if you have never done it before it is possible that one of the connectors or a line came off inside the tank.
Not a problem. Just let me know.
Your welcome. If the system does not find any problems eventaully it will turn the light out. Did he tell you what codes were stored in the system?