I'm having similar issues with 2.0.2 on my headless server. Here's some sample output:
*** TCP socket (ECServer) listening on 0.0.0.0:4712
*** Server UDP socket (TCP+3) at 0.0.0.0:4664
*** TCP socket (TCP) listening on 0.0.0.0:4661
*** Client UDP socket (extended eMule) at 0.0.0.0:4672
Adding file /home/fuzzix/.aMule/Temp/001.part.met to shares
Adding file /home/fuzzix/.aMule/Temp/002.part.met to shares
Adding file /home/fuzzix/.aMule/Temp/004.part.met to shares
Adding file /home/fuzzix/.aMule/Temp/006.part.met to shares
Adding file /home/fuzzix/.aMule/Temp/008.part.met to shares
Adding file /home/fuzzix/.aMule/Temp/010.part.met to shares
Adding file /home/fuzzix/.aMule/Temp/024.part.met to shares
CServerSocket: connection refused or timed out
CServerSocket: connection refused or timed out
CServerSocket: destroying socket 0x87f30c0
CServerSocket: destroying socket 0x8800c58
CServerSocket: connection refused or timed out
CServerSocket: destroying socket 0x87f30c0
CServerSocket: connection refused or timed out
CServerSocket: destroying socket 0x87f30c0
CServerSocket: destroying socket 0x87f30c0
CServerSocket: connection refused or timed out
CServerSocket: connection refused or timed out
CServerSocket: connection refused or timed out
CServerSocket: destroying socket 0x8821768
CServerSocket: destroying socket 0x8800c58
CServerSocket: connection refused or timed out
CServerSocket: connection refused or timed out
It goes on like this. I can request that amuled try connectiing to another server through the remote gui and the refused/timed out response is almost immediate.
I upgraded to 2.0.2 and used it successfully until a few days ago when I started having this issue. I can't think of anything I did which might have affected it - I don't remember installing anything on the system since then. As I type this I got a connection to a server - file this one under "intermittent"...

To check it's not my ISP or an IP blacklist I attempted a connection from this box with the graphical client (I run X here - Slackware 10.1, Linux Kernel 2.6.11.7, curl 7.12, wxGTK 2.6). It connects to any server immediately (with LowID as no ports are forwarded to the desktop). The server list is from a frequently generated server.met file so most servers I attempt connection to should be up.
Anyway, the problem machine is a P3/700 with 512MB RAM and about 1.5GB free on ~/. Slackware 10.1, Linux kernel 2.6.11, curl 7.12, wxGTK 2.6. It also runs a httpd on port 80 and sshd on port 443 (don't ask

) I can provide any additional information required (read as: I'd really like to provide more information. What's relevant?)
Thanks.