I don't agree with this. That isn't bad at all.
The signal level at -65dbm is not great.
I do agree with this.
The error message indicates the connection attempt is being refused (actively), rather than timing out.
Are you sure there is not another device responding to the pings? That "connection refused" is a firewall response, and the w5100 has no firewall, (edit:) and I presume the wifi shield has no firewall either. Disconnect the Arduino from your localnet and try the ping again.
BTW, my routers do a similar check when assigning localnet ips with dhcp. They do a ping to the ip about to be assigned to a new client, and if a device responds within a half second, it marks that ip lease as "busy", and gets another free ip from the ip pool.
edit: I use PuTTY in RAW mode to test http connections.