The old Alcatel modem .. what is the model number? Is it setup as router or is it a pure modem.
The new TC cannot connect to the old 2003 Extreme by wireless..
I would remove the old extreme entirely.. plug ethernet from DSL modem to the WAN port of the TC and try the setup again..
Do a factory reset before you start. I recommend the following.
Start from a factory reset. No files are lost on the hard disk doing this.
Factory reset universal
Power off the TC.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the TC to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
N.B. None of your files on the hard disk of the TC are deleted.. this simply clears out the router settings of the TC.
Setup the TC again.
Then redo the setup from the computer with Yosemite.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg TCgen5 for basestation and TCwifi wireless name.
If the issue is wireless use TC24ghz and TC5ghz with fixed channels as this also seems to help stop the nonsense. But this can be tried in the second round. ie plan on a first and second round of changes to fix this.. hopefully.. I will point out other steps that can be round2.
2. Use all passwords that also comply with 1. but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
If you still have trouble I need specific details on the modem and if you are using pppoe in the TC to do the setup.
I would strongly recommend a new modem.. even though the old alcatel are great modems.. in fact many old modems of that age are amazing.. that is now 12 years old.. however they were tricky.. the Home and Pro models are only 10mbit connections and were wired with reverse polarity on the ethernet.. which works sometimes and not others.