|"My tablet was now plugged into a telephone wall jack."|
There isn't a tablet made today that can use a dial up connection.
"I was told that the LAN would ensure a stronger signal"
Are you talking about an Ethernet connection? LAN simply refers to a Local Area Network, not a connection type. You are safer using a wired connection than a wireless. Where was this connection anyway?
They would have had to either hack your tablet or have a keylogger installed to get to your Dropbox files. The likelihood of this is extremely doubtful.
Are you worried about security or did something actually happen to cause you concern?
message edited by THX 1138