what is a box called that stores lots of hard drives so that other pc can access them?

Network attached storage?

http://www.newegg.com/store/SubCategory.aspx?SubCa...

Though there are many factors result in a slow computer like infected by viruses, or too many installed program, you can still try the steps below to speed up your computer according to my own experience: 1) Uninstall the programs that you don't need. 2) Delete the files you don’t need 3) Use the disk clean-up option in Windows to regularly clean up the system junk files. 4) Turn off System Restore feature. 5) Use a reliable registry cleaner to clear the windows registry. 6) Regularly scan the computer for viruses and spyware. 7) Remember to disable some unneeded startup items. Once you have done the above point, follow the steps below: 1)defragment your hard drive- A GOOD solution to speeding up your computer by effectively managing the files on the hard disk. 2) Turn on the real-time safe-guard feature of your anti-virus program to protect you computer at any time. These are what I have done when trying to speed up my computer, and wish it helps you, too!

I believe what you are looking for is a server.

A bay or server i think.

an enclosure