Recieve/send texts via my broadband wireless modem, (mobile signal/reception is poor).

I was wondering if someone could advise me on this: My house is in an area
that has very weak coverage, by any mobile network. So it is impossible to
carry on a fluent text chat with anyone.

So I am wondering, is there a way I can send and receive the texts to my
phone, by, say, connecting wirelessly to my broadband modem?

Alternatively, is there a way I can set up a computer program so that my
texts are received, via the 'net, on my PC?

I know that some mobile service providers let you send texts, via the web,
to mobile phones. So perhaps the reverse can also be set up somehow?

This might work for me provided the program provides a ringer alert whenver
a text is received.

Many thanks...