I presumed your old computer was still around.
If you have the PostgreSQL/8.3 directory you may be able to recover your data, though it might depend on the state your computer was in when you were copying the data over.
Make another copy of the file putting it in C:\Program Files\ of the computer you want to restore to.
So now you have a C:\Program Files\PostgreSQL\8.3 directory that contains all of the appropriate subdirectories.
Then follow the directions of
this PDF to reinstall PostgreSQL on your machine; pretend like you just uninstalled it and just follow the reinstallation part and it should work properly.
This part of the Postgres FAQ that I linked explains how to backup a PostgreSQL database. Which part of it confuses you?