Lime Wire » Download Out-Of-Date Installers
Yours is a problem that's difficult to discover what it is at fault. 'Something' is giving a firewall effect. If still connection problems, check the tips here If LW 4 Will Not Connect (click on the blue link) since solutions for LW 4 are a little different to LW 5.

You may need to remove the firewall rule for LW in XP's firewall & re-add it.

May I ask how old your modem is? If it's oldish, might be faltering, being inconsistent. Using battery or mains power for modem?