The tds relay has 2 diodes in it,it does two functions.(2 relays in one unit)
1) runs the lift pump when the glow plugs are in operation ie cold start.
2) receives an output from the alternator once engine is running and this enables relay to close and lift pump to operate,hence the bad hot starts as lift pump not running until engine fires.
3) connecting a + live to the existing live wire connection at lift pump will make the glow plugs operate constantly (I do not know how ?,just read it on another forum a few weeks ago,something to do with the relay having these two separate functions built into the one unit.
4) although your relay will not latch and operate glow plugs and then hence the in tank pump will not supply fuel,your starting problem is lack of fuel to injector pump.The car if it has fuel should cough and fart about and chuck out clouds of grey smoke and eventually fire up if it has fuel with out the glow plugs.
You could run a live to the lift pump,under the black oval cover in the boot,I will post up a link to a site where some one fitted a facet pump to replace their lift pump,this should get it to start,but the relay has to be able to latch on its second side to enable engine to run (output from alternator).