Mulan,
Out of 9 questions
here, your post answers only first 3 questions. Answer the remaining questions below so that we can guide you better:
1] What is your Operating System ?
2] If Win98/ME/NT, have you upgraded UPS10.dll successfully?
3] Can you read Unicode Tamil Letters here? தமிழ் எழுத்து தெரிகிறதா?
4] What Tamil Software are you using to type tamil texts? (Murasu Anjal/eKalappai/Kural)
5] What is the Exact Version of that Tamil Software?
6] What Editor are you using to type Tamil Texts?
7] Have you checked the Encoding & Keyboard of the software setting? What are they?
8] When you type using Unicode, what is the result you get?
9] What browser are you using?
Most common mistake people do is not downloading appropriate Tamil Software.
The best one is eKalappai. It's freely available
here.