First, you have to consider the exact number of songs, their format, mp3 example, and how much memory they take up on your old computer, what file folder contains them and to what do you want to copy or transfer be that an external disk drive on a DVD disc or an external hard drive or if you want to use computer software to transfer the files using a USB 2.0 universal serial bus to carry the data.
Some programs are designed to allow a computer user like yourself to copy all or part of one computer to another with a few simple steps.
If you are interested in this subject just Google it using such key words as copy files from one computer to another computer and thus you will have your selection to choose from.
The reason I recommend Google to search for this is that it is extremely reliable. Not that Yahoo!Answers isn't reliable, far from it but Google can help you in a pinch when you need an answer in seconds flat.
I use Google all the time and Yahoo!Answers 24/7.
This is what computers were designed for, to get answers to questions, not the run around so take advantage of Yahoo!Answers and Google and any other source you know about to find out about computers, iTunes, and QuickTime player Safari, and all that as well as millions of Windows stuff that will make your computer time the best time it can be.