Is there a problem with having a router/wireless internet ...?

at your home yet being able to sometimes visit a friend who has no ''unsecured enabled'' connections at their house and you can't afford a wireless adapter/contract....what I mean is, I have already spent $168+ between spending $110 for tech support alone at $2/minute on my old isp [dialup] on hooking up the landline, then realizing the old isp simply couldn't help me, having to pay over $18 to hook up to the new isp only to find out I couldn't get a connection with THEM either......btw....the phone dial tone is fine and my modem is too....the internal one....please help.