If one PC is connecting as normal and the other giving problems then I would suggest that the phone line is OK and Wanadoo's service is OK otherwise BOTH the PC's would have the same problems connecting. I would think the answer lies with the PC which is having problems. Have you tried re-installing the drivers for the modem or even transferring the known to be working modem from your other PC into the problem one and seeing if there is any improvement. It may also be a noisy line and one modem is more sensitive to this than the other. Contact BT and have them increase the 'gain' on your phone line to see if this makes any difference. It might be worthwhile using the modem cable from the working PC as well just in case the cable's faulty.
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