TCAS works on time to impact or near-miss.
I believe the Traffic Advisory is given 45 to 20 seconds before impact and the Resolution Advisory follows 10-15 seconds after(RA is only given if BOTH are aircraft are S-mode equipped).
No transponder:
Aircraft can only be tracked by primary radar. Clouds and ground clutter hinder tracking of aircraft.
Mode A:
Aircraft tracked by use of secondary radar. Atc may indentify aircraft by an ATC issued code (Squawk). No RA provided
Mode C:
Aircraft tracked by use of secondary radar. Atc receives the aircraft's pressure altitude information (1013mb/2992in.) and may indentify aircraft by an ATC issued code. No RA provided.
Mode S:
Aircraft tracked by use of secondary radar. Atc receives the aircraft's pressure altitude (1013mb/2992in.) information and may indentify aircraft by an ATC issued code. Also the each aircraft has a unique code and also transmits information such as aircraft type and current performance.
RA provide if all aircraft in conflict are mode S equipped (able to handle a Max. of three aircraft in conflict at one point in time)