Change LW to manually connect not auto connect (LW's menu Tools>Options>Connection & untick option box & press both Apply & OK buttons.) Then go to File menu & choose connect. Wait up to an hour for LW to settle down. Any difference?

Your laptop modem is a dialup so there shouldn't be any problems there. If you have a lot of incomplete files & particularly if you use the 'Resume' function for them they can take a long time to settle down, resulting in queuing for much, much greater periods & also playing havoc with your connection quality. Resume means the files will seek out for resources every few mins & if can't find any will eventually give up, with a status of 'Awaiting Sources' (instead of the normal 'Need More Sources'.) Resume can be very effective though, if not used on too many files. It's safer to allow LW to settle down & search manually for resources.