Lael8
Hello;
Allow me to welcome you to the HP forums!
Don't know what you consider the most "cost effective solution" but to me, that would mean wasting the least amount of money up front ... for a start.
If you just take your PC somewhere, they will charge you Time and Labor just to examine it and determine if the monitor has gone bad.
To save that charge, you would need to determine that yourself, as follows:
1) Borrow a monitor from a friend
2) Hook that to your PC in place of your monitor
3) If the monitor displays, then your monitor has gone bad
4) If the monitor does not display, then swap the monitor cable with the one from your friend's monitor
5) If the monitor NOW displays, your monitor cable is bad and you need to replace it
6) If the monitor still does not display -- most likely, your monitor is OK
7) Hook your monitor to your friend's PC -- it should display OK -- confirming the monitor is OK
Now, as to losing the pictures from your drive -- YES -- there is a very great risk of losing them.
Standard practice in most PC repair shops is, rather than "wasting time" backing off the contents of a customer's drive, they just use a factory image to completely reset a PC. That means that everything on your drive has then been erased.
It would be possible to get SOME of the data back, but only the data that was not overwritten by the imaging, and to do that, you would have to use data recovery software.
So, BEFORE, you take the PC anywhere, do the following:
1) Locate a friend with a working PC (same one as has the monitor?)
2) Buy a USB-to-Hard-Drive adapter
3) Remove the hard drive from your PC
4) Connect your hard drive, using the adapter, to your friend's PC
5) Copy the files and folders you want to save from your drive to your friend's PC or to a USB stick
6) Shut down your friend's PC and disconnect your drive
7) Return the drive to your PC case
Good Luck