Be sure to scroll down... there may be more than one question on this page!
Yes, it does matter. By switching the ground, hot, and neutral wires you may inadvertently produce an electrocution hazard in the metal frame of the fluorescent fixture. You will have to remove the cover on the fixture that hides the ballast and determine which wire in the cord is hot. Generally, the hot wire on the ballast is black, and the neutral is white. The other colors are the wires that connect the ballast to the fluorescent tube holders and to each other.
There is another issue, though. These non-commercial fixtures are generally not UL-approved for hard wiring unless there is a manufacturer's fact sheet that says it's OK. So if there is no indication that hard wiring is approved, you will have to install new replacement three-prong plugs at the now cut ends of the power cords. These plugs are available at any hardware store.
To solve the ON-OFF problem, simply install an outlet box(es) near the fixtures, and wire the boxes so that it is controlled by a single wall switch!
Generally speaking, a flickering fluorescent bulb means that one of the pair of bulbs in the fixture has bought the farm. My philosophy of sensible repair is to always replace both tubes. Fluorescent tubes have such a long life and are so inexpensive that it makes sense. Not that it's the most economical solution... it is just a practical viewpoint from someone who has been paid to do this type of work for others. To receive a second call in a month because the other of the two bulbs has gone bad is neither desirable from the customer's point of view ($$) or mine (pride in a job done right).
Fluorescent tubes can be tested with a multimeter by performing a continuity test across the pins on either end. However, this is not a completely reliable test, since a loss of gas can also cause fluorescent failure. So for the handyperson, the best way to test the tubes is to install them in another fixture that you know functions. If you have a 4-tube fluorescent fixture, this is easy... remove one of the still-working pair of fluorescent tubes and replace it with each of the questionable tubes, one at a time. 99% of the time it will be one of the tubes that is the culprit.
However, if both tubes are functional, the problem is with the ballast or starter. The starter is replaced first, and if that does not solve the problem, the ballast should be replaced.
And a special note for the uninitiated... don't spend all day looking for a starter in your fixture! Most modern fluorescent fixtures do not have starters, so if it is not "in your face" (it looks like a small gray cylinder) your fixture don't have one. They are never hidden, though they may be concealed slightly by the tubes.
There is a good article on troubleshooting ballasts, using a multimeter here: http://www.doityourself.com/stry/how-to-troubleshoot-electronic-ballasts
Last newsletter, MR from Pittston, PA wrote about a problem he was having with a noisy fluorescent fixture. Some of our readers offered suggestions that are worth noting... and passing on...
GB suggested replacing the inexpensive magnetic ballast with an electronic ballast. However, he was wise to note that the replacement ballast might cost more than the fixture!! (In my research I found that electronic ballasts, besides being more expensive, are also more sensitive to heat than magnetic ballasts. Since some fixtures have the ballasts located right next to the bulbs, this heat MAY be an issue.)
KG offered two suggestions concerning possible problems with the wiring. First, if the fixture was as the end of a long run of wire, there might be a voltage drop that could cause a "dimming effect". Fluorescent fixtures are generally not dimmable... trying to do so can either cause them to go off OR produce some vibration in the ballast. KG also wondered if the installer properly grounded the fluorescent fixture. Old incandescent fixtures were typically not grounded, and lack of a ground could cause a ballast to become noisy!
CF and SR suggested checking that the ballast was securely mounted. Many ballasts vibrate to some degree, but a loose ballast will be even louder! CF suggested checking the entire fixture, not just the ballast. SR went a step further to suggest using a heat-resistant silicone caulk if tightening was futile.
There was wide consensus, though, that the cheaper the fixture, the noisier it will probably be! Thanks to all!