Not sure if it is as easy as that: go to your Front-Page/Home. Turn EDITING ON and add back your blocks. Besides that I guess you can not DELETE the Admin Block, you can only HIDE and DOCK it. So you should be able to show it again here. Reset your THEME to Moodle Standard, as it might be your theme is not capable of showing docked blocks. And have a look at the Admin-Block's under the ACTIONS-Icon where it says CONFIGURE ADMINISTRATION BLOCK as you can set where/on which pages this Block should be displayed.
Rosario