first and foremost that is a huge voltage drop. some drop is expected and even planned for on LARGE properties but typically a non-issue on your standard residental lot (reason these controllers put out 26-28v although these are 24v solenoids). i would guess this particular zone has been out of commision for some time, low voltage at the solenoid can be just as hard on them as high voltage....wears them out FAST, hence a solenoid reading 0ohms. a good solenoid depending on brand should read between 25-55ohms. the voltage reading dropping to 0v under load and 16v wide open suggests a bad nick and or almost completely severed field wire (ghost voltage). unfortunately these are very hard to find, even with wire tracers/locators. locator has a tendancy to trace right over top of problem without much of a signal drop and or spike. not impossible but takes a very attentive tech who knows how to tweak his locator instead of just blasting a signal at full power. i would suggest grabing a can of paint, renting a wire/valve locator and marking your wire path even if you dont pick up on nick or break in wire mark the path. if the system was installed with color coded multistrand try testing voltage on that same wire at several points, working your way back to controller until you find point at which you get at least 24v. if your wire is all single strand red field wire and white common this task gets alittle harder for average homeowner. all and all if this valve is remotely close to the controller or if you have a spare wire that runs close by......run new to controller or use spare.....there are several other things to mention but thats a start.