In the novel, the Machine gets turned on 31st December, 1999. But what year was it when the SETI received the signal? (or how many years did it take to build the Machine?)
In the novel it's not especially clear, but the machine appears to have taken about a decade (and possibly between 5-15 years) to build which means the signal was (probably) received around 1989-90.
IT TOOK years, it was a technological dream and a diplomatic nightmare, but finally they got around to building the Machine. Various neologisms were proposed, and project names evocative of ancient myths.
Eventually, it came to half a trillion dollars a year for some years, roughly a third of the total military budget--nuclear and conventional--of the planet.
and as the Machine nears completion;
The daily headlines in The New York Times were, by any dispassionate measure, more bizarre than any in the now defunct National Enquirer a decade earlier.
The script indicates the signal was received in 1996 or early 1997.
Ellie seems to join SETI in New Mexico in 1993
EXT. NEW MEXICO DESERT - AERIAL SHOT - NIGHT
A 1967 T-Bird travels swiftly along a dirt road through the moonlit desert. The VIEW CLIMBS, WIDENS to include a huge radio telescope, and as we come around we see an even more stunning sight: 30 more of them.
SUPERIMPOSE: SAPPORO, NEW MEXICO - 1993
When Drumlin visits it's an election year (so presumably 1996)
DRUMLIN Very well; since my appointment he's been made interim director. ELLIE Really? Congratulations, by the way. DRUMLIN I'm surprised you even knew it was an election year.
...and the signal is received shortly thereafter.