Yeah cable/wire connection. Check at battery, and where the jump start terminal is, as well as at the starter and engine ground.
You may have a fusible link primary wire at the starter that has partially failed too. Look at the small wires for any sections that are darkened or feel less rigid than the rest of the wire.
Another way to check this is if you catch it in the act, leave the key on, door open, open the hood, reach down to the wires going to the starter and move them around a bit, see if the affected systems suddenly come to life. You'll hear the ignition chime start, DRLs come on, and probably hear a couple of relays close when the connection is made. If that makes it work, you've either got a bad connection down there or a bad link. Fortunately on the 3.1 they are easy to see/mess with from up top, you don't have to roll under the car to try this.
When links don't burn through completely they can cause problems like this. And everything they supply is affected, while other systems work fine. I'd check all the regular connections first though, before focusing on that.
Why would it act like it did? Well, if this is the problem, the temp that morning was just right to make the link's insulator contract and pull the damaged wire section apart. There might be just enough there to carry a little current, but not enough to operate the systems. Trying to put power to the headlights through a bottlenecked wire creates a lot of heat. The insulator warms up, sags, and the wire strands inside expand and make more contacts. Suddenly the lights come on, and everything is normal again. Until the next time. Same can happen with a weak cable connection, but the mechanism is a little different.
Here's a burned link on a Buick starter that caused similar symptoms. No headlights, no ignition, only specific primary power affected.
