Would it be possible for me to take my internet DSL connector and my laptop to another phone number (location) and have it work? The modem(?) is an old Sprint 645 series.
The reason I’m asking is that the house I sit has their own ISP connection that I can’t use, and I’d like to take my laptop with me to the house I’m going to and plug it into their phone line but not run up their phone bill.
I don’t think I’m making this very clear, I hope you get my drift. 
Nope. It’s hardwired to your phone line.
No, it’s not hardwired, but the physical phone line has to be “provisioned” with DSL service.
If your friend’s line is already provisioned for DSL, they’re paying for DSL.
It sounds like the house you’re watching does have DSL. If so, you should be able to plug your laptop into their DSL “modem” and get a connection.
It’s a virtual cross connect at layer 3 which can only be done on the LT port of the phone line belonging to the account holder, which makes it as good as hardwired.
Ah, sounds like we’re referring to two ends of the same wire. You’re talking about the nuts and bolts of provisioning over at the DSLAM side of things, and I’m talking about stuff at a subscriber’s home - the DSL bridge, or what the OP was referring to as the “connector.” (I’m assuming they weren’t talking about a Cat5 cable!)