Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
If the audio circuitry doesn't work well enough to produce sound from microphone input, and if the CD player won' spin up nor turn the CD, then a vital voltage is either missing, or deficient, or loaded down by a shorted component.
Whether this problem is in the power supply part of the device (as is fairly likely, I think), or in some part that is loading down that voltage that is evidently missing (or the CD drive would turn), I am not sure can be determined, without a good audio electronics technician taking apart the device a bit and examining it.
(How old is the 'singing machine' of whatever maker and model, that you have? it might be covered by warranty, perhaps... if new enough. Let me know maker name at least, and its age, please. I will tell you how to proceed further, as you wish and as the information indicates.)