what version of auto cad are you using? Are you trying to copy/clip into a new file? Or an existing file? If it is a new file just save as the old file (the one with the layers and stuff in it) as the new file. Also try cutting instead of copying sometimes that works. and then there is always the import file

Have you tried making everything a poly line with a little thickness? Also sometimes what you are seeing is what you will get try rendering it to see what it will really look like