What information does a pilot have about aircraft operating on an intersecting runway?
As the question mentions, good situational awareness is an excellent safety tool. ATC is responsible for runway separation at towered airports, but pilots can play an important part of backup in the case of a human mistake.

The United pilots may or may not have been able to see the Atlas 747 on TCAS, as the terminal building that obstructed their view could also have blocked the transponder signal. TIS-B (Traffic Information Systems - Broadcast), a part of ADS-B, provides traffic both in the air and on the ground. ADS-B was not available in 1996, but if the same situation happened today and the United aircraft had an ADS-B signal on the surface and displayed TIS-B information, they would see the Atlas 747 on their displays. Whether or not that information would be useful to avoid an incursion in a cluttered runway environment is unclear.

The FAA is implementing a system to provide exactly the type of warning you're describing. Runway Status Lights (RWSL) use surface RADAR and lights embedded in the pavement to detect conflicts and alert pilots that a runway is unsafe to enter or take off from. In this situation, the United pilots would have seen red takeoff hold lights to inform them that the runway is unsafe for departure. The FAA plans to have RWSL operational in 17 airports, including Chicago O'Hare, by 2017.