What exactly do you mean when you say they won't start? Does
anything happen at all? Do you hear the disk working and then sudden
silence? Does Windows crash or give an error message? Does a window open
and then freeze?

Think back to when you first used it successfully. Did you change anything in
the configuration at all or share any files? Did you do anything similar in
LimeWire before it stopped working?

Do you have any so-called antispyware or antivirus software? Which ones do
you have? A couple have been known to interfere with BearShare and
LimeWire by mistake. Do you have any firewall or anything at all related to
protection of any type?

Aside from that it is impossible to guess because I don't know anything about
your setup like which versions of BearShare, LimeWire or even Windows you are using.