While there could be many different things wrong...
First forget the router until connected. RIght now you have no internet at all, so wait on the router as it should be easy to fix the wireless once you know whether you have internet at all or not.
If possible make sure all cables are good.
Connect direct to modem.
Try to find out what means what on the lights of your modem (important).
Turn everything off and hook it all up and install/setup as instructed. Making sure to go to the net conn and properties/change connection and then(in networking tab depending on your OS) highlight tcp/ip then right click properties then select "obtain ip addy automatically" and click ok. Make sure that even if it is already selected that you click ok and let the pc write for a minute. Continue with the setup according to the modem instructions. At this point it will probably mean powering down and restarting everything and trying to connect. Try it. If nothing then you need to look back in the net conn and find the details about you ip addresses. There should be a place that will list your dns servers and ip address. ip lease info etc. (Sorry Im on a ME machine right now or I would tell you exactly how to get everywhere, plus I run XP in classic mode) You need to see that this is all "proper" with appropriate looking numbers. If not, you are not resolving (receiving) an ip address from your isp properly which is most likely their fault if you are set up properly. If everything is kosher looking then there is probably a harware issue.
Check the lights on your modem and see if the one that indicates "stuff coming from isp" is functioning as it should, is it solid, flashing, off? This light tells you about your connection to the isp and whether you have gotten an addy or not.
If still nothing, try one last "power cycle." Turn everything off and pull the power to the modem for a minute then repower. Do not turn on your comp until you see the light I mentioned doing its thing. No light no internet. If you get a light try to connect.
If still nothing, go to start run type cmd then in the DOS window type
DOS will try to send info to that site and will tell you the results.
0% loss means you are connected
100% loss means you arent.
At this point if you arent online you need the isp.
Get an isp that you can call 24/7. Even on holidays.
Have them ping you and see what they say.
Once you are online the wireless should be so easy, however there is a small chance you may need to upgrade the firmware on the router if its a linksys.
I havent been on dsl for 3 years but was on it for 3 years. Im a little rusty with the dsl specs but hopefully this helps.
Someone mentioned pppoe earlier. Unless dsl is different than when I had it pppoe is NOT always neccesary with dsl. I never used it that I know of. Maybe it is an automatic function? You shouldnt have to mess with it at all.
Make sure you explain to your friend that what he wanted (to just order it all up and then plug it all together) never works.