Your pix at home should not see any icmp packets, or any other cleartext packets, as the ipsec vpn is from your pc to the 3000, not from the pix to the 3000. You say you can connect using the client, but what do you mean by connect - you pass user authentication, or something else?
Is there a conflict between your home lan ip address and that supplied by the 3000? You may want to disable split-tunneling on the client end, if the 3000 config is not already set to do so, to eliminate that issue from arising as you are trouble shooting this issue.
Set the 3000 up for nat-t (aka transparent tunneling) if not already done so. If you do not want to use nat-t, then on your home pix code this: fixup protocol ike-esp which would allow the pix to properly nat your ike and ipsec traffic to the 3000.
Let me know if this was of any help, or if I could help you further.
