Sometimes after market screens will only work with the most updated version of iOS. Start there. Also, try a soft reset, let is sit for a minute, then check. If still nothing do another soft reset. If still nothing... time to check the solder points on the board. You may have a larger issue at hand.
Restore disks can be produced from any computer running Vista. Ask a friend. Have you legally purchased Vista? If you can demonstrate that then you can download a Vista ISO and mount to disk. You will have to do a repair from a recovery, or install disk. If you need your computer to work for basic functions while you research this visit pendrivelinux.com. Create a bootable flashdrive. It'll be a life saver.
The repair is very difficult. You will spend as much getting the tools and LOCA as you would spend on a replacement screen. Yeah the glass to replace is cheap, but you need cleaning agents to clean the frame when you remove it. You need a temp controlled heat plate/heat gun, a special wire, tons of patience, cleaning agents to clean the LCD once removed. Then LOCA and align the new glass to the LCD. Once you have that it will need to be cured in a UV box. Then you need a very strong adhesive to replace the frame. Every step of the way the failure rate is high. Most break the frame during removal. The LCD is very likely to get damaged. And assuming you make it that far, chances are the glass will shift during curing and the LCD won't be aligned correctly. Assuming you got that down, there is also a good chance that that digitizer won't function when reassembled. This repair really should be down in a static and dust free environment. My advice is to leave this repair to the repair shops. Unless you are okay...
Good chance that the phone corroded while it was in storage. Remaining water, although not a problem at the moment given time will raise the humidity inside the phone. Which can cause damage over time.
That screw thing always comes off. You want to be careful to still ground that plate because that is the real purpose of that thing being there, I think. I've had everything from reception (wifi) to no boot problems, to no problems at all and that thing was the difference.