Well, from your description, I'm not sure 'how' you have stored your music on the old computer? First, what type of computer do you own and what did you buy; second, do you have iTunes on the old (and new) computer - since you have not done a 'sync' I'm assuming that you are not using iTunes to transfer your music to the iPad - answers to these questions will help others give better advice to you on this issue.
Although iTunes can in a 'pain' to use, the program does have advantages and can certainly help organize your music - if you go that route, then you would need to get your music into the media library (under 'music') of iTunes and then transfer this music to iTunes on the new computer; transferring your music from iTunes to the iPad can be done via a sync or manually (I tend to do the latter, i.e. rip my CDs or DL MP3s into the iTunes library, then simply drag onto my iPad icon in the left sidebar). If interested in going the iTunes route, this
ARTICLE may be of help (despite being a little dated).
NOW, if you have figured out another way(s) to get your music on the iPad (e.g. various cloud services), then please let us know - always looking for iTunes alternatives -
