Kyle Bateman here with BinaryWave.com
If you have accidently closed a Web Part within SharePoint and have no idea how to revive it, don’t panic; The Web Part is still in the Web Parts directory simply titled “Closed Web Parts”. To get there we must start by clicking on the “Site Actions Tab”, as seen in the photo below.
Select the “Edit Page” option from the drop down menu in the “Site Actions Tab” on the top right of the page.
Then you must select the zone to which you would like to add the “Closed Web Part”.

Select the “Add a Web Part” option from the zone in which you have chosen.

This will then open the “Add Web Parts to Zone” Feature.

Note: you will not be adding a Web Part, you will be selecting the “Advanced Web Part gallery and options” feature on the lower right part of the page.

Now we click and open the “Advanced Web Part gallery and options” feature, here will find the “Closed Web Parts” that we were looking for.
F.Y.I. There’s a good chance that you may have to sort through various Web Parts that have been closed and not deleted. Make sure that you delete the “Web Part” as opposed to just closing it if you have no intention of using the said Web Part again.