prints - Why do my scanned images have lines across them?

As you can see in the example, my scanned images have horizontal and vertical lines across them. They are very noticeable in dark areas of the image. The original print is a 4x6 matte finish print. Scanned using a very basic HP PSC 1210 - 600 x 2,400 dpi scan resolution, 19,200 dpi interpolated, 36-bit color.

I am using Windows 7 scan wizard, and have tried 200dpi, and 1200dpi. I could adjust the images in Photoshop, but am trying to scan it correctly the first time.

Please tell me what my issue is, the original print finish, scanner, settings, anything else?