|If you have a BIOS password installed then I suggest you boot into the BIOS (setup) screens and at least temporarily disable it.|
BTW, If you can still boot to the CD drive without entering the BIOS password then it is useless because it can be circumvented. Instead use a hard drive password after you get running again.
I don't think WiFi would affect the restore. WiFi has to be configured after the fact.
The third disk would probably be any bundled apps including the HP crap.
If your wording above is correct the screen is ASKING if you have the third disk. Have you tried clicking on Enter or Escape at that time?
How old is the computer? If you know anyone with an HP with similar specs you could borrow their restore set and use it to restore your computer.
Alternatively, you could install Windows 7 or 8 64 bit. Your laptop should be able to run 8. See the link below for some pricing.
I see you asked in another post about the BIOS password.
Watch the screens at startup to learn how to enter the BIOS (setup) screens. May be F1 or F2.
Once there you move around with the arrow, up/dn, pg up/dn, esc and enter keys.
You enter the password to change it to nothing by removing it and when the line is blank hit enter. Be sure to save when exiting (F10).