I had come up with a theory, but I'm not sure if all of it fits anymore. I'll have to pay attention while I'm writing it in case I'm sure something has changed since I first thought of it.
I assumed that he had made plans from home to meet his friends after he got there Sunday night, but had to change them (either before leaving home or after he was picked up) because his father said he wouldn't take him that night - but had errands to run the next morning so he could drop him off when he left about 6:30 Monday morning. When his dad unsuccessfully tried to get him up for an hour, I can see him telling him, "I'm leaving now, and you'll just have to wait until I get home to go."
When Dylan got up later, he could have tried calling his friend/s to say he missed his ride, but got mad that he couldn't get a signal or the phone was dead and just decided to walk/hitchhike (just to show his dad he didn't need him!) he ma or may not have grabbed his fishing pole to bring along, depending on what they had planned. It's possible that he first left because he knew there was no signal at the house, and tried to call after getting down the road a bit, and then discovered his phone was dead.
I guess what happened from that point would depend on who picked him up. It could have been someone passing through who took him with them; it could have been a neighbor who offered to take him to the friend's house but did something else; it could have been a neighbor who DID take him to the friend's house and something happened after he was there; it could have been a stranger who did either of the previous things. It could have been that something happened along the road (animal, car accident, other kind of mishap). He could have grabbed the pole to go fishing wherever it was that someone said was right by the house, and fell in, met someone untrustworthy, or any number of other things.
I'm still not so short of ideas that I'll start considering anyone in the family yet. Those ideas are usually easy for me to come up with, and I'd rather think of any alternatives first.