I'm not familiar with the "Open Local Collection" option you mention but I've always just copied and pasted. So I'd do this
1. Open the original Sketchup file.
2. Select instances of all the components you want.
3. Copy them into the clipboard. (Ctrl C)
4. Close the file and open the new file
5. Paste the clipboard (Ctrl V)
6. Now you can delete the pasted instances if you want, the components are still in your components palette.
*** EDIT ***
Jeez you guys are quick.
I agree with h3nry, the simplest way I know to do this is to copy and paste. Open up the old drawing file, select the component you want to use. Copy using your favorite method (CTRL-C, Edit/Copy) and the component will be in your clipboard. Open up the new drawing, and paste (CTRL-V, or Edit/Paste).
Works just like Excel or Word, or most other programs that use the normal windows clipboard.