That is the actual Form. To be able to pick and choose which fields  are
on the form  you need to edit  that form in SPD and replace the ListView
Web part  with a DataForm web  part. Simply open a copy of the form for
editing, delete the existing web part, and then click on Insert >
SharePoint Controls > Custom list  Form. That will insert an Appropriate
Data Form web part where you can delete individual fields from the form.
Then save the new form and associate it with the list using the
Supporting files tab on the properties panel for the list.

Well, I did what you said, and now I have another issue. When I try to add a
new item, (NewForm.aspx) I get an error message saying "Invalid Page URL:" I
think there is something missing from after associating the new form  with the
list. (I did do the requisite IIS reset jsut to be sure.) Reverting the
NewForm.aspx and EditForm.aspx back to the site definition also doesn't work.

Are the forms all stored in the Forms directory under the list  that is
using them?

Also, did you work on the original forms or edit  copies as my message
instructed? You should never edit the original pages in SharePoint.

Finally, after you reverted the forms did you go into the properties of
the list and change which forms the list is using? If not the list is
still trying to use the new forms even though you reverted them back.

Now I am running into a new issue. When I try to attach a file to an item in
the list, I get an error message that states "This form  was customized not
working with attachment." The error message appears twice each time I click on
"Attach File." Any ideas on how I can resolve this?

You can't. it's a known issue  when you use a custom edited form  as the
NewForm.aspx or the EditForm.aspx of a list. Only the default form
allows attachments.