I am posting a second answer because I am now taking a very different interpretation of your problem. In a comment below my first answer you state:

Your function seems to correct one type problem with fraction. But I am more looking for something able to display TeX in the exact form I write them. Probably MM is not the right tool to use. I am disapointed.

I assumed that you were looking for TeX conversion of arbitrary expressions generated by (evaluation in) Mathematica but if instead you simply want TeX for expression in "the exact form I write them" you may be able to use Strings, e.g.:

The string was created using standard input methods. \\[Times] was entered with Esc*Esc. Here is the input in copyable form:

"\!\(\*FractionBox[\(1\), \(2\)]\)\[Times]\!\(\*FractionBox[\(3\), \(4\)]\)" // TeXForm 

And the output formatted by MathJax:

$\frac{1}{2}\times \frac{3}{4}$

Critically this method avoids interpretation of your raw input into e.g. Times and Power, thereby bypassing those "pretty printing" rules that were changing your expression in an unwanted way.

I am posting a second answer because I am now taking a very different interpretation of your problem. In a comment below my first answer you state:

Your function seems to correct one type problem with fraction. But I am more looking for something able to display TeX in the exact form I write them. Probably MM is not the right tool to use. I am disapointed.

I assumed that you were looking for TeX conversion of arbitrary expressions generated by (evaluation in) Mathematica but if instead you simply want TeX for expressions in "the exact form I write them" you may be able to use Strings, e.g.:

The string was created using standard input methods. \[Times] was entered with Esc*Esc.

Here is the input in copyable form:

"\!\(\*FractionBox[\(1\), \(2\)]\)\[Times]\!\(\*FractionBox[\(3\), \(4\)]\)" // TeXForm 

And the output formatted by MathJax:

$\frac{1}{2}\times \frac{3}{4}$

Critically this method avoids interpretation of your raw input into e.g. Times and Power, thereby bypassing those "pretty printing" rules that were changing your expression in an unwanted way.