When you say you upgraded to broadband, is it the same ISP, or someone different?
You need to check the required server addresses for your new provider. You can only send e-mail via your own ISP, although you can receive from anyone.
So for example, if your old provider required the (fictitious) address;
But your new provider requires;
you can see how you would have a problem.
It is also possible, that even though you may have stayed with the same ISP, the fact you have changed to broadband, requires a fresh address.