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
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.
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.