Hello dear, Tg can be determined by DSC, the state is not important, since this analysis not shows dependence on it. About the your second question, there are so many properties, but to me is very important, rheological analysis.

You must run DSC scan with cooling to can determined th glass transition for viscous polymers.

Best

Thanks for your answers, Yes, I took the DSC, it dose not show the TG but it has given the Tm (melting temp) at 110 oC. I'm just curious about how can I get this by changing some parameters or sample loading. 

Perhaps, glass transition temperature of your polymer is very low. Changing the heating range of DSC can be useful.  

What properties you want depends largely on your expected applications. Rheology is a useful technique to better understand the polymer. 

Another possibility, is that you cannot observe the Tg is related to the range of temperature employed, if you start your DSC analysis from -70 °C and you cannot observed it, you have to use a capillary rheometer for finding the Tg value, since it employ liquid nitrogen and the temperature range is lower than -70

All the right suggestions are given. For measuring Tg you must start minimum 20 degree C below Tg. In this case you have to cool it to very low temperature as you do not have any idea. .

We use a TA Instruments Q2000 DSC with a RCS 90 cooling unit for Tg by DSC experiments on both elastomers and thermoplastics. Primarily, we perform the experiment to ASTM E1356 (elastomers) equilibrating at -90°C to 23°C  with a ramp rate of 10°C/min. If we are interested in viewing thermal history, state of cure or all transitions we will run a Heat - Cool - Heat experiment. The DIN Tg spec actually calls for a H-C-H ramp to eliminate thermal history of thermoplastics.

Regardless of the experiment, if we are going to ramp above room temp on an unknown, we always run a TGA first to determine at what temp a 1% mass loss is observed. We never ramp above this temp value w/the DSC to avoid decomposition contamination in the DSC cell.

If the DSC data indicates that multiple transitions are occurring at the same temperature we run the unit in a modulated mode (which often separates the 1st and 2nd order transitions).

Thank you all for your suggestions, it helped me a lot :)