Beirut — There was no fanfare when President Amin Gemayel and his entourage left Beirut Monday, bound for crucial talks at the White House aimed at salvaging two things: Lebanon's very survival as a nation and the credibility of United States foreign policy.
Mr. Gemayel's departure was not even announced until after he had left. (Israeli Prime Minister Menachem Begin canceled his visit to Washington, planned for next week, citing ''personal reasons.'' See Page 5.)
It was a stark contrast to his first widely celebrated trip after being elected last September, when it appeared Lebanon was about to be pulled out of eight years of chaos and the US had a virtual diplomatic monopoly in the Middle East.
Both have crumbled with time. And some Middle East analysts are now predicting it may be too late to save either one.
The basic problem is that neither the US nor the Gemayel government has been able to resolve the Lebanese crisis.
Meanwhile, events in Lebanon have overtaken the two key policymakers, who are mutually dependent: President Gemayel needs the US clout to help sort Lebanon out; President Reagan needs Lebanon to make his first foreign policy success.
Mr. Gemayel left behind a nation disintegrating on several fronts:
* Bitter fighting among the ''mountain people'' began yet again, the sounds of artillery shells echoing as far as Mr. Gemayel's presidential palace in the capital.
The current round of trouble goes back more than 10 months, but is based on an almost tribal feud of more than one century between Maronite Christians and Druzes, members of a secretive sect of Islam. Both moved to the Shouf Mountains centuries ago, but attempts by both sides to expand in the countryside overlooking Beirut and the Mediterranean led to disputes.
The current clashes serve as a symbol of ongoing sectarian strife - among many other rivalries - and undercut the stability and nationalism needed to pull Lebanon together. Residents generally consider themselves Christians, or Sunni Muslims, or Druzes, before thinking of themselves as Lebanese.
* The strife also symbolizes the fears of the majority Muslims about the intentions of the minority Christians, who dominate the government. The fighting first broke out shortly after the Palestinian massacres last September, allegedly at the hands of Christian militiamen of the Phalange Party. Many Muslims, particularly Druzes and Shiites, are concerned about a massacre against them, especially if they try to hold on to their areas.
The massive Israeli military machine - which controls the Shouf - has not been able to stop the fighting, and it appears doubtful any other force could do it, either.
* For the first time since the Israeli invasion last summer, street fighting broke out in the heart of Beirut last week, when authorities tried to evict Shiite squatters from the abandoned Jewish quarter. Families refused to go, arguing they had no place else to live.
Shiite militiamen came to their aid, while the Lebanese Army was called in for what turned out to be its debut as a force able to restore law and order. Seven persons were killed and 21 injured in seven hours of fighting, as the Army pounded the area.
It may have amounted to a minor victory for the Army, but the psychological damage over the long term may be high. Shiites called for a strike Saturday and managed to close down all of west Beirut. And the Shiite Amal (Hope) organization called for the resignation of the government.
* The economy is in tatters. It is no longer just a problem of the absence of reconstruction funds, which rich Gulf Arab nations have made conditional on Israeli withdrawal from Lebanon. Now business is so bad that several companies which survived eight years of anarchy have begun to lay off workers.
Economic stagnation has started eating away at even the most successful and resilient part of Lebanon's infrastructure: banking. Activity has slowed by 30 percent, according to a Beirut press report.
* De facto partitioning of Lebanon now seems inevitable, since the Israelis want to cut their casualties by withdrawing from the Shouf to a line some 20 miles south of the capital where they can consolidate and reduce the vulnerability of their soldiers to bombings and guerrilla attacks.
Syria is expected to keep its troops in Lebanon, meaning the country would be carved up into three zones: Israelis in the south, Syrians in the east and north , and pitifully small Lebanon consisting of Beirut and the mountain environs.
And without any progress in Washington this week, it could remain that way indefinitely. The situation is so critical that some diplomats speculate that Mr. Gemayel, the first President to grow up in independent Lebanon, may be the first to oversee the end of his country as it is now known.
These are among the many things to be discussed during the sessions Thursday and Friday at the White House.
The most immediate problem is Syria's refusal to talk about withdrawing its 40,000 troops from Lebanon. Secretary of State George Shultz had hoped to obtain an agreement like the one negotiated with Israel in May, which has not been carried out because it is conditional on simultaneous Syrian withdrawal.
Lebanese Foreign Minister Elie Salam and various US diplomats have suggested there may be some unspecified ''new ideas'' put forth, possibly including a dialogue with the Syrians divorced from the framework of the Lebanese-Israeli accord.
But Syria declared again on Tuesday that it was not interested in playing ball. Damascus Radio quoted President Hafez Assad as telling French parliamentarians that ''there is no possibility that we will alter our position.'' And the state-controlled press blasted Mr. Gemayel for continuing to turn to the US.
The US and Lebanese appear to be hoping something will come of the new Syrian-US ''working committee'' set up during Mr. Shultz's visit to Damascus earlier this month. But there is little ground for optimism, since the Syrians claim it is only a channel for clarifying their position.
Lebanese officials claim Mr. Gemayel will tell the Americans that his government put all its cards in the US initiative and that the Reagan administration now must push hard to see it through. Western diplomats counter that it is not a matter of the US being unwilling, but rather unable to crack the impasse.
And without progress on regaining all of Lebanese territory, through the withdrawal of foreign forces, it appears doubtful the other problems facing Mr. Gemayel can be sorted out. That would leave both Lebanese and US foreign policy facing major failures, with ramifications that could stretch on for years.