I have a pair of PSP 1000 who register "ghost inputs" on the analog even if the analog module or the rubber.... conductive... thing... are not installed, i think theres something wrong with the motherboard.
Have you tried to fire up the console without these pieces installed?
Man we were gonna have a game night at my buddy's house but he wasn't feeling great so he canceled, which throws my dinner plans up into the air, so I guess it's time to order a pizza or something