You have to use the SMTP server from your new ISP. The old SMTP server is likely your old ISP's and as such can only be used if you are on their service.
I'm using Outlook 2010 w Windows XP Pro SP3.
Until recently I have been connecting to the internet through various mobile hotspots or mobile internet sticks, and my email functioned properly. I started connecting to a wireless router/DSL modem combo provided by my ISP, Telus and now I cannot send emails. I get an error saying Outlook can't connect to my outgoing SMTP server. I did not change any settings in my Outlook email and the outgoing SMTP server settings still work properly when I am connected at other locations.
I have gone into the router setup and disabled the firewall, because I thought it might be interfering, and it did not solve the problem. My email host has web access which still functions normally. I have called Telus and they did not have a solution.