I have no internal monitor on my laptop, it was severely damaged by someone stepping on it. One attempt to access BIOS using HDMI  to factory reset was to disconnect the the monitor from the laptop. So I have no monitor on the laptop. Another attempt to see if I could access BIOS was using a VGA cable and I could not. I shut it off and turned it back on to find it installing a SERVICE pack. And I was extremely frustrated, having been trying to access BIOS through an external monitor for a long time and stupidly shut my computer off while it was installing this service pack. Then I connected it back through HDMI and now I get nothing. I have always been able to access the OS through HDMI and VGA before I shut it down during the service pack install. So, I'm guessing I fudged something up pretty bad. The thing is I can't see anything to know what I fudged up. So I'm at a complete loss.

I'm sure you need to know that it's a Sony Vaio VPC series. I'm sure you'll need to know more but seeing as I cannot see anything to find out, it will be difficult. But I am sure I can get the JOB done, just not really sure what I will need.

I also have the geek squad recovery discs, but I can not see these either through HDMI or VGA.

I have the feeling I'm pretty much out of LUCK unless I buy a new screen, which I'm not even sure I should do if I've completely messed the laptop up. So, really any suggestions would be great. I am honestly willing to try anything. How much to you think the laptop is worth?
Given that you have used VGA and HDMI before, likely you have something more that a smashed display. You should be able to connect to an external display just using the buttons on the keyboard.

Some of the Sony Vaio VPC series were made some time ago and are now worth very little.  If yours is one of those, you might want to get a used replacement from eBay and transfer the files off the drive. Otherwise, the cost of a new screen may be almost the same. Depends on the MODEL number. But even with a new screen, you don''t know if that is the only problem.