In general if the part is compatable with the new system you can reuse it. Cases almost always are, you need to check what board form factors it supports(atx, micro atx) , but may not provide adequate cooling. Memory/CPUs/boards depend on compatability. The PSU must provide enough power for new parts. I wouldn't use a harddrive over 5 years old for anything important. And old DVD/harddrives that are IDE won't work on most modern boards.
Post what you have then we can tell you.