Once you confirm that your PSP is version 1.5, you will need to connect your PSP up to your Windows machine via a USB cable. You can either use the one provided with the PSP package or one of your own. While connecting the two devices together should be simple, I continuously run into a 'USB Device not recognized' error, which many others appear to have been plagued with as well. The reason for this is unknown, but to bypass the problem just ensure that you select USB Connection on the PSP device BEFORE plugging the cord into the computer. Otherwise, the connection will fail.
Note that if you cannot bypass this error, you will have to do a bit of tweaking and probing to get everything working again. In my case, I found that you can get a connection by repeatedly removing and reinserting the USB connector four or five times. When that didn't work, I was able to get a connection by removing all USB devices from the Device Manager and then refreshing the hard device manager. This is accomplished using the following steps:
Click Start → Settings → Control Panel
Double click the System icon, select the Hardware tab and click the Device Manager button
Locate Universal Serial Bus controllers at the bottom of the list and expand the menu
Right click on each option, and Uninstall (repeat until there are no more items in the list)
Right click anywhere on the Device Manager list and select Scan for hardware changes