As a dial up user you should not operate as an Ultrapeer. Go to LW's Prefs>Speed & tick Disable UP capabilities & press the Apply button.
Don't use the Resume/Find Sources function on many (if any files) at a time. Especially on dial up. Doing it on many files will have side-fx; your downlds will queue up for much much longer than usual. Also your LW connection quality would be affected & on dial up could drop right down to the red.
If you wish to continue downlds, do searches for their topics again if needed. This is the 'Best' & most effective way to find sources & new/fresh sources for your downlds.
After opening LW, let it settle before you do any searching. Depending on how many shared files & how many incomplete files you have this may take some time.
Some hints: A well set-up LW can start to automatically continue its dwnlding after it's settled down perhaps 2 out of 3 times you open LW.
Optimising LW & Maximising Uplds & Dwnlds A (1st post only) & also
Part B which is even better & last & least are
search & dwnld hints. The latter one I've been thinking about re-writing for some time. That's just for playing it safe. eg- I show all speeds & qualities.