I do not want to use
mathptmx package since using this LaTeX=>PDF is not not compiling. Please suggest me to achieve Times New Roman Fonts and math environment, anything other than
A word of advice about the TeX distribution: disk space is not a big issue nowadays. Unless you're running TeX on a very small device, do a full install.
In addition to egreg answer, there is also the MathTime Professional 2 font, whose lite version is freely available. IMHO it is the best looking math font for Times, and a number of prefessional math journals use that.