You are obviously have DCC/connection to bot trouble.
However, your message gives very conflicting information regarding when the issue happens.
Is it, you can only DCC chat while on the same IRC server as the eggdrop?
Is it you can only DCC chat while you (and your client) are on the same computer?
Is it, you can only DCC chat one of 4 eggdrops?
If it's the first one, what IRC servers are you using?
If the second, this is 99% likely to be because of hostmasks (Security). When on another computer, your hostname/ip (the unique address the computer is assigned while on the internet) will change. Eggdrop tracks people by there hostmask, which is a combination of IRC nickname, username (provided by identd) and the hostname/ip. It looks in the form nickname!
username@hostname.ip. It is formed into a mask, that can be used while trying to match users. This mask is likely not matching you when you move to a new computer. To fix this, add your new ident using "/msg <bot> ident <password> <original-nickname-when-you-where-added>"
If the third, have you been added to the other bots? To access each bot, you need to have a suer-record, and the correct flags. This task can be automated with userfile sharing. However, simply linking bots is not enough. See the relevent sections of
http://www.egghelp.org/ for information on setting this up (if wanted).