Mary,
The filament in your daytime running light is probably broken, and when it gets jiggled around and makes contact, it'll light up. The current flowing through it will likely hold it there unless it gets jarred pretty hard - that is until the current flow stops, like in the flashing of the turn signal.
These bulbs are fairly inexpensive and available at any auto parts store. The hard part is getting to them. If you have fairly small hands, the easiest way to get to them is to lift the hood, and turn on the headlights to lift them. Then remove the hood stop (if memory serves a 12mm wrench will do the trick). Take care not to change the position of the locking nut too much, juest loosent it about a 1/4 turn to free up the stop. With the stop removed, you can reach down and forward to find the bulb fitting. Turn it 1/4 turn to release the tabs, and pull it out. You probably won't be able to get it above the front bumber, but there's enough slack in the wires to give you room enough to change the bulb. Then put the bulb fitting back into place, replace the hood stop, and you're set.
The alternative methos involves jacking up the front of the car, and perhaps removing one front wheel, sticking your hand through the brake cooling duct, and possibly removing some additional plastic panels. Never tried that, as my hands were small enough to go from the top.
It shouldn't take more than ~15 minutes the first time you do it, and I'd bet I'll do the next one in less than 5.
Good luck.
Craig-o
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