With my home ISP I can receive but not send. With my office ISP I can send and receive.

I have 2 gmail accounts in my notebook. When I am in the office, using ISP “X”, I can send and receive emails without problems, from both accounts. When I take my notebook home, I use a different ISP “Y”. I can receive but cannot send, from either of the 2 accounts. I get this message:
“6:54:18 PM [email protected] [SMTP]  MailClient.Accounts.SocketException: Connection failed due to the following reason: 6:54:18 PM     “A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond 74.125.206.108:587”
6:54:18 PM    at MailClient.Protocols.Smtp.SmtpSendCommand.Connect(WorkerStatus status)
6:54:18 PM    at MailClient.Protocols.Smtp.SmtpSendCommand.Execute(WorkerStatus status)
6:54:18 PM    at MailClient.Commands.Command.Process(WorkerStatus status)”
I had this problem with Thunderbird, I changed to eM Client (free version) and it’s the same.
I read several posts who experience the problem of not being able to send. I tried to change the SMTP port (587/25), the security policy (all of the 4 on offer), all to no effect.
If I use GMail on line, I have no problem.
It looks like ISP “Y” (at home) has blackmailed both Thunderbird and eM Client…
Anybody can help?
Thank you!
Maurizio