when I look at this question to me like you got a modem/router from one isp, have since moved to another and their modem doesn't do any the fancy stuff the other one did, and since your switching from dsl to cable there's no way to use the original modem as a modem, but you still want to share your connection and use the wi-fi off the original modem. and while it's possible to plug in the cable modem and other computers in. and configure the old modem to act as a switch/AP instead of a dsl modem, it can't do NAT in that state; which is the key component of connection sharing. and I'm guessing the reason your asking about needing connection sharing is because the cable modem does not do that. one way you could find out if the cable modem is actually doing NAT and thus is ready to share the connection once there's a way for more then one computer to be physically connected to it, or not which then would require some other device to sit between it and the computers to do the NAT for the connection sharing to work. would be to check what Ip address your getting if it starts with 10. or 192.168. when your connected directly to the cable modem (without the dsl modem) then yes it is, and it won't be a huge issue to use the DSL modem; you just need to set the dsl modem to use the an ip on the same subnet as your computer got from the modem and turn off the dhcp on the modem and then it's ready to go as a eithernet switch and Wireless Access Point. but if you get an IP that starts with some other set of numbers then the two I got listed then that means to share the connection you need some device to do NAT that would sit between the two modems. and unless you have a wired router sitting around then it's going to cost just as much for a wired router as a wireless one and be a whole lot less hassle to yourself a wireless one. (if you do got a spare working wired only router, then use that to set up a shared wired connection between the cable modem and the router. then you can follow the same steps as if the modem was doing NAT, just remember to plug the reconfigured dsl modem into the wired router, not the modem)
if your wondering what NAT is, it stands for Network Address Translation. and it is the mechanism that allows multiple computers to share one "public" ip address, as it translates the requests from the private ip's your computers gets to and from the one public ip you get from your isp. an analogy here would be sending postal mail out to addresses, where there is not room on the label for an apartment or suite number. people who live in a house are unaffected by this as each has a unique street address (aka only one computer on the connection), but people in apartments will not be so lucky, as they all have the same street address as all the apartments are in the same building,(aka multiple computers on one connection). so the mail carrier has no choice but to drop off all the mail at the front office as that's all they have is the street address to go on. NAT would be like the person in the office who examines the letters to determine which apartment the letter was intended for and sorts out the mail for each apartment. it sorts out which packets are meant for what computer so the can get routed back to the computer that was requesting the data.