The bolt for the battery broke and I lost power to everything. Put a new bolt in and power is restored but now my radio, air conditioner and stabilitrak won't come on. Any suggestions?

A Toyota Avalon radio is bolted in place in the dashboard in order to prevent theft. If you want to replace the radio with a more updated stereo or an in-dash DVD player, you'll need to unbolt the old radio. The bolts are concealed by the dashboard's trim panels, and there can be one or two other objects you'll need to temporarily remove as well.
Step 1 Shut off the power to the Avalon by disconnecting the negative battery cable.
Step 2 Pry off the central register panel above the radio on the dash. Use a trim stick or a flathead screwdriver with tape wrapped around the blade. With the register panel gone, pry off the dash trim panel that surrounds the radio. Disconnect the electrical connector to the clock.
Step 3 Remove the control panel for the air conditioner if it is blocking your way to the radio's mounting screws. Remove the front console trim over the air conditioning console, disconnect the mounting screws and remove the control panel.
Step 4 Disconnect the mounting screws to the radio using a small hex wrench. Put the screws aside in case you can use them to install the new stereo or other device. Pull the radio out of its space to find the electrical connector and antenna lead in the rear of the unit.
Unplug the electrical connector and antenna lead, and remove the radio. These connectors will be used with any new radio or stereo that you'll install in the old radio's place.

Check all Ground Points. Battery cables can look good but not be. You should use a DVOM to check for voltage drops from battery to where ever the grounds go to. Also use the DVOM to check the battery cable terminal and post. Put one lead on the battery post and the other on the cable terminal. The DVOM should read 0 or very close to it.

You need to look under the hood, located the Broken/Missing Serpentine Belt. Repair the damage the belt did when it broke and put a new one in. The Alternator is not turning and that is causing No Power to get to the systems and more than likely, when it broke, it knocked some wires around.

Fig. Alternator wiring connector locations







Fig. Alternator bracket and bolt locations

1. Note the radio security code and the radio presets.
2. Disconnect the negative battery cable, then the positive.
3. Remove the power steering pump.
4. Detach the wiring from the alternator.
5. Loosen the through bolt, then loosen the adjustment locknut. Then loosen the adjusting bolt.
6. Remove the alternator belt.
7. Remove all mounting and adjusting bolts and then remove the alternator unit.
   

To install:

1. Installation is the reverse of removal.
2. Adjust the alternator belt tension.
3. Enter the anti-theft code for the radio.

Hope helps (remember rated this).

If it's the 3.1 or the newer 3100 the starter should just be a couple 13 and 15mm bolts. Plus the nut for the cable. Hope this helps.

check fuses and change mechanics

Ignore smart a$$ comments.
Disconnect negative battery terminal.
Remove front right wheel.
Remove splash guard.
Place jack under engine.
Remove left engine support bolts from body.
Remove engine support plate bolts from engine.
Unbolt air conditioner pump and move it out of the way.
Get under vehicle and remove steering pump bolts and move it out of the way.
Remove 6 crankshaft pulley bolts, should be 12mm.
The engine support bracket shoud come off now.
Remove the main crankshaft bolt.
Remove crankshaft dampener.
Remove the timing cover bolts and take off the covers.
Take off the old belt & replace with a new one, don't use a previously used belt.
Make sure the belt tensioner is installed correctly.
Put all the stuff back on.
Get a Haynes manual, pages 3-41.

my radio ad a/c works only same times for ten minute and then turn off and no works maybe until next day

You can get a "Chilton" book that will show everything for your vehicle or try googling "1984 Buick Riviera belt diagram" and there may be a site that has it posted.
Let me know if this helps.

Such items don't break on their own.
In any case, a good mechanic should be able to remove a broken retaining bolt, but access to it may be poor, depending on the model. Those I have dealt with are accessible by removing the plastic inner fender on the right side of the car.
I don't know what they are claiming is the relationship between a broken retaining bolt and a broken belt, or the air conditioner "going out", or who or what broke the bolt.
That bolt is commonly used to rotate the motor by placing a socket or spanner on it. It is quite a large bolt, and should easily stand being used to crank the motor around. So unless it has been used to prevent the crank turning at some past time while doing something else to the engine or transmission, I fail to see why it would break!