THE failed assassination attempt Aug. 29 against Georgian leader Eduard Shevardnadze could prove to be a turning point in this troubled country's struggle to restore order to its affairs. The authorities have pounced on suspects in the wake of the car-bomb explosion that narrowly missed killing Mr. Shevardnadze, the head of state. They are trying to stave off more violence before presidential and parliamentary elections on Nov. 5, which they hope will mark the end of four years of turmoil in this former Soviet republic. But Shevardnadze's advisers nonetheless say they fear another attack may be imminent. No one has yet been charged in connection with the bomb blast outside the parliament. But four men, close to prominent parliament member Jaba Ioseliani, head of a private army known as the Mkhedrioni, were detained last week - including the deputy head of the security service, Temur Khachishvili. His boss, Igor Giorgadze, was dismissed by Shevardnadze, in a move approved overwhelmingly by parliament Sept. 2. Meanwhile, in a search of Mr. Ioseliani's parliamentary offices, police say they turned up large quantities of guns, grenade launchers, detonators, and drugs. ''It is impossible for them to rebel openly against the government now,'' says Petre Mamradze, Shevardnadze's chief of staff. ''The Mkhedrioni have no force now to make great trouble openly.'' But Georgia's political situation remains fragile. Supporters and opponents alike say stability still depends directly on Shevardnadze, the former Soviet foreign minister who returned home from Moscow to take power in 1992. ''He would be irreplaceable here. Nobody knows what would happen if he went,'' says one Western diplomat. ''All the international institutions and donor countries are looking to Shevardnadze to lead Georgia for at least another three or four years.'' Government officials describe a shadowy opposition to the head of state - organized criminals, warlords, and hard-line communists such as Pantelemon Giorgadze, father of the dismissed security chief, poised to seize power if Shevardnadze had been killed. Were they to succeed, claimed Zurab Zhvania, secretary general of the pro-Shevardnadze Citizen's Union coalition, ''It would not just mean killing the head of state, but the entire system that has been established.'' $10-a-month salaries Government leaders hope that the upcoming elections, on the basis of the new Constitution, will help the country develop guarantees for law and order. Shevardnadze is expected to win the presidential poll, but the outcome of the parliamentary vote is less clear. Opposition groups could benefit from popular frustration with the economy, local analysts say. The government insists the economy is picking up: Certainly, the sidewalk cafes on shady Rustaveli Avenue, Tbilisi's main thoroughfare, have opened recently. But average salaries are still well under $10 a month. Gas used to fuel the stoves and heat the homes of all urban Georgians. But it has been unavailable for more than a year since Turkmenistan lost patience with Georgia's failure to pay for supplies. A quarter of a million refugees from civil war in 1992 to '93 add to the country's economic woes. They cannot go home until an agreement is reached on the status of the rebel region of Abkhazia on the Black Sea coast. Georgia has offered a federal arrangement, but Abkhazians seek a looser confederation. The government is hoping that Moscow, which aided the rebels in the war, will pressure their allies to compromise. But Moscow's intentions in Georgia are unclear, government officials say, fueling distrust and fear. Pipeline to prosperity In that context, the prospect of a pipeline through Georgia linking a huge oil field in neighboring Azerbaijan with Europe (see story at left) is of more than just economic interest to Tbilisi. ''If the pipeline comes through here, it means that the whole area becomes of geostrategic importance to the West, and we want that as a balance to Russia,'' says Irina Sarashvili, leader of the opposition National Democracy Party. But concerns about the country's future are bound to make any oil executive think twice about entrusting output to Georgia. The government has had trouble dealing with armed gangs, opposition politicians say, since the warlords - including Ioseliani - brought Shevardnadze to power in the first place. They invited him to come home after they overthrew elected President Zviad Gamsakhurdia. The Georgian leader has since edged most gangs out of influence. As a result, Shevardnadze has become the only person with the status to rule. His supporters say such a concentration of power was inevitable, drawing comparisons with French President Charles de Gaulle after World War II. But others argue this is a mistake. ''If Shevardnadze had been killed, it would have been complete chaos, and it would have been his fault,'' says Nodar Natadze, head of the opposition United Republican Party. ''He has done his best to hold all the threads of power in his hands.'' Progress is measured in small units. ''We are still in anarchy, but the first signs of normal life are appearing,'' says Mr. Mamradze, the head of state's top aide. ''If you don't hear automatic-rifle fire in the streets every night any more, it means democracy is beginning.''