Let's address your primary concern first. Provided you do not format, install anything on, or damage your hard disk, you will not lose your music. Since you cannot turn your system on as long as you don't physically attack your computer your music should be fine. Worst case scenario would have you putting that drive in another system to retrieve your music. (if your issue was due to a lightning strike / power surge then there may be a problem and is outside the scope of your question)
There are many things that can cause a system not to power on. A bad power supply, a bad motherboard (the voltage regulators are shot), a bad power cable, etc. In your case you're getting power to the system but only get an amber light.
Given the lack of information here it's very very difficult to determine the cause. Consider these things:
1. Is the light on before I hit the power button?
- If the light is not on before then the computer is doing something when you hit the button. - it's giving you a yellow light - which means your power button is working at least. If you purchased this system from a PC vendor such as Dell, HP, Compaq, etc. then you can look up the user manual / help section for your computer and use this information to narrow down your issue.
2. Do the fans spin and stop, keep spinning, or don't spin?
- again you're looking for signs of the system doing anything. If the fans spin then stop, then you know your power button is working and connected correctly and can rule that out. If they continually spin then you know your power supply is probably good and now you're addressing a no post issue.
3. Does the system emit any beep noises?
- unlikely or you would have mentioned it. The idea in these situations is to do what we can to get the system to respond. Even if we can't see anything on the screen beep codes are helpful and can tell us what's going on with the system by comparing the beep sequence to the troubleshooting guide for your system.
Without knowing more these are the more important questions, assuming you have a good power cable and power source, and will help you understand what the computer is really doing. If your system does have a bad power supply, motherboard, CPU, or memory, then you'll need extra parts to test with or will have to take it in to a repair shop to have it diagnosed, but I'll list some common troubleshooting steps to help you eliminate everything else.
Unplug the system, hold the power button for five seconds (clears latent power on the motherboard), put on my trusty anti-static wrist strap, and re-seat the memory and all the cables. If it still does the same thing I would unplug cd rom, and test. Then my hard drive and test. Then bring the system down to what we call minimum requirements. For most systems this is one stick of memory, the cpu, the motherboard and power supply. Everything else is removed or disconnected, to see if you can get the system to power on at all. If you hear a beep sound at this point (missing video card assuming it's not on board) then you know something you pulled is causing your issue. If you don't get the beep then you know one of the components left is the culprit and I would start with having a PC store test my power supply.
I apologize for the length.