Was the phone working when you received it and before you made repairs?
When you say it is not turning on, I assume you have already tried connecting to iTunes... (did you try just the basic logic board and dock flex?)
There's not a lot to "test" on the Tristar, it is mainly a communication chip so most of the lines are for serial communications. You need an oscilloscope or logic analyzer to really see what's going on. Now, if the phone is dead and it worked before your repair attempt, then I would start at the beginning and check the area surrounding the connectors, especially the battery. Then check if you have shorts on the main voltage rails (PP_BATT_VCC & PP_VCC_MAIN). Then check PP3V0_TRISTAR & PP1V8_SDRAM to see if they are powering the Tristar IC.
Check those out and get back with updates.