Does arcing with fluorescent lights indicate an open neutral?
This is a double problem.  It is a ground fault of the lights, which should normally be handled efficiently by the wired grounding system (and not the water pipe).  Unfortunately it is not, which reveals faulty wiring. 

Normally, all current is supposed to return on the neutral wire, with wired grounding only as a safety shield.  The wired grounding is meant as a "catcher" to assure that any ground-fault current returns on the ground wires and does not resort to using water pipes etc.  Those should never come into play, not even in fault conditions.  The water pipe bonding (grounding electrode) exists to ground lightning and ESD, both natural electricity sources.  

You can "kill the symptom" by fixing the ground-fault on the fluorescent lights.  But I wouldn't do that just yet.  I would use it as the "canary in the coal mine" to chase this problem. 

The real problem

Your ground wiring (or maybe neutral) is very broken.  First, check your neutrals for continuity.  I expect they are intact, as the water pipe/earth path is probably not capable of flowing enough current to power 8 fluorescent lights.  If you disconnect the water pipe strap, do the fluorescents in the garage go out?  If  you run a power tool also, do the fluorescents desperately flicker and the power tool stumble??  If those things work OK, that means the neutral system is probably intact.  

Now onto the ground.  I expect ground defects, and realize this is not the end of the world -- you can retrofit ground. 

First, I'd give a careful once-over to the main panel, just to make sure everything is in order.  Obviously your ground-bus to grounding-electrode strap is in good order, because removing it makes sparks, and that also proves the bond between your ground bus and your neutral bus.   In this main panel, you may see neutrals and grounds all jumbled together.  This is sloppy, but legal in the main panel only because there only, neutral and ground are bonded together.  That will not be the case in subpanels. 

The subpanels

The grounding here will be the crux of the matter. Correct is that the subpanel is fed from the main panel by 4 wires -- a ground, plus neutral, plus 2 hots - so 4 wires in total, with ground and neutral separate.  (occasionally you'll see only one hot; so one less wire).  The neutral and ground feeder go to separate neutral and ground bars, and those are isolated - they are not bonded, and any bonding straps or green screws are removed.  Each circuit has its neutral and ground going to separate bars.   That is correct. 

However it's quite likely you will find 3 wires - 2 hots and a neutral.  One approach is to "bootleg ground", i.e. attach all the grounds to the neutral bar (like is done in a main panel). However, that would cause any fault current to return via neutral, which would not cause your symptom. 

The other "3-wire" scenario is where the person means well, but doesn't understand the importance.  In this case, they correctly keep separate ground and neutral bars, and do not bootleg/bond ground to neutral (ok so far). But they fail to run a ground wire back to the main panel: they simply drive a ground rod into the dirt and attach the ground bus to that.  They expect dirt to carry back any fault currents to the main panel, via the main house's electrode.  That doesn't work.  Dirt is a very poor conductor, and will actually hide a dead-short bolted fault by not allowing enough current to flow for the breaker to trip. 

I think that's the scenario you are going to find; either that or they did something much more awful, like abuse a water pipe as the subpanel ground rather than running a wire.  You don't want to flow current on pipes, unless you're really into galvanic corrosion and replacing pipes a lot. 

The solution in any of these "3-wire" scenarios is to run a separate ground wire, and recent Code changes allow you to run just a ground wire.  The ground rod doesn't hurt, it's just no replacement for a ground wire.  The rod and wire do different jobs, and one can't do the other's. 

Fixing the ground faults

Every device is supposed to take power from "hot" and return it all to "neutral". When devices have insulation problems internally, they may start leaking power to other places they should not.  This would "electrify their metal chassis" and hurt people or start fires, if it was not for grounding.  This is why grounding exists.  

I disagree with my colleague regarding the source of ground faults in fluorescents and other HID lighting.  Fluorescent lighting is commonly used in basement, garage and other utility space, all of which are protected by GFCI in a modern home.  It would be anathema for a modern electronic ballast to have any ground leakage, even 1ma, because with 10 fixtures, that would be 10ma, which exceeds the trip threshold of a GFCI.  I argue electronic ballasts are the solution, not the problem.  However, cruddy old magnetic ballasts (the heavy kind full of transformer windings and drippy tar - don't try to salvage one unless you really like tar) - those are highly prone to ground faults, in my experience.  

You can switch to direct-wire LED "tubes" if you like, however I am not impressed with the build quality of the cheaper ones.  I am very impressed, however, with the quality and price of modern fluorescent ballasts and the latest tubes from mainline manufacturers.  As such, I am sticking to real fluorescent for now.  Get any respectable brand of electronic ballast that matches your light's wiring, then get nice 90 CRI tubes that match your ballast.  You will not believe how nice things look in that light.