Have you ever wiped the recovery partition?
If you are still able to boot the machine then make sure you back up all your files, documents, Pictures etcetera first.
If you are still able to actually boot the machine then install MiniTool Partition Wizard Free and run the program - check the Type column under the resulting information for the installed disk and check if there is a mention of (Recovery Partition).
If there is mention of a (Recovery Partition) then you are in business so long as the Recovery Partition has not been corrupted in some way.
If you are not able to boot into the Desktop and install the previously mentioned program to check then you may as well try to restore to factory via the Recovery Partition anyways (you won't know it's there but again it will work so long as there is no corruption).
Here's how:
If the original OS was XP ...
1) Power the computer on
2) Press Ctrl + F11 keys at the same time when you see Dell logo screen and then release both keys at the same time
3) You should now be at the Dell PC Restore
4) Click Restore (caution message appears informing of data loss)
5) Confirm
6) Progress window -> wait -> should get recovery success message
7) Click Finish -> Computer should reboot -> go through normal setup prompts
If Vista / 7 ...
1) Power the computer on
2) Press F8 key (should now see Advanced Boot Option menu)
3) Select Repair your computer -> Enter
4) Specify language -> Next
5) Login as user with Admin privileges -> OK
6) Select Dell Factory Image Restore -> Next
7) Tick checkbox YES (Reformat hard drive and restore system software to factory)
8) Next
9) When finished click Restart and go through normal setup prompts
Failing this I can't really help you - if Dell says they can't supply the Recovery Media then you are going to need an installation disk / USB and a license key.
Let's hope the Recovery partition is not wiped / corrupted! Good luck