formatting it was a bad idea.
if you did that and ERASED the HP, partitions called, Recovery
now the F11 Recovery feature is gone for ever.
id bet those were not bad, I bet the junior tech, replaces them in that order guessing at your cost, as is so common today.
but lets forget the past, it's gone.
if the F11 key (or what the manual says) is dead its dead.
that takes what? a good HDD, next. if its good and the CD drive works, (many dont now) then you can disk install the OS.
but you have no disks, do you,
all HP new they sold the disk set called the HP media kit
if you didnt buy them when new, they are long long gone.
this is a 2014 PC correct, the service guide page 17 tells you how to use the HDD, magic, recovery.
http://h10032.www1.hp.com/ctg/Manual/c04329428
if you erased the HDD , that will be and expensive fix.
never erase any HP HDD , unless buying a used one to use.
or you get to buy windows again,
or run Ubuntu linux 16 , for free. (a great choice)
if if you must erase, just do the root of C:/
clearing out all of windows.
and not touching this.
here is W7
do not erase the 2 partitions on the right ever. (if not rich)
think of them as VIRTUAL INSTALL DISKS.
cuz they are.
http://www.pcdied.com/W7-FMT.JPG
good luck
best is upgrade to w7, or to w10 . Vista is now a DEAD OS.
best is to avoid xp and vistafor ever.