For Yahoo Mail
Try this stop gap :
Open in your browser
web yahoo messenger.
[url]http://webmessenger.yahoo.com/[/url]

Log in with your
Yahoomail Id and password.
Yahoo messenger web page will open.
Click Yahoo mail on top right.
2.

If Yahoo mail is accessed, program other email such as
Gmail account also.
3.
Mention you modem model/make in all replies.

1. First disable firewall ( only for testing )

2. Wrong MTU and MSS setting in ADSL Modem,
Correct the setting MTU = 1492 and MSS=1452

3. Try using some other browser like Opera , Firefox

4. Try after disabling Internet Security related software.

Also mention whether Yahoo mail Id is Yahoo.com or Yahoo.co.in.
Feedback.