2005 chevy impala

sounds like hood hasn't been opened for a while, check coolant level , trans fluid level while running in park, and look at wire connectors at battery posts and nearby fender ground connections

The A/C should blow cold air and the heater hot air. If you only get it on one side, are your vents on the dash open? Do you have dual climate control? Perhaps the controls are not turned on on your side. If that is not the case, see if the door under the dash open to allow air to get to your side of the dash.

duel climate control, a/c works on passenger side, but blows heat on driver side, but blew cold briefly.

OK, so the A/C works. That is good. Next the passenger side works, that is another positive. The blower works, so another check off as what is working. The list of possibilities is decreasing. There may be a switch that is bad, but if it works momentary, than it is working? The controller door is at fault. Either something blocking the vent, a spring is broken, or a control door is not being moved to direct the flow of air. I have not torn into the dash so I am not sure if reaching the door controllers is accessible from under the dash or if the dash panels must be pulled to look at it. A controller wire may be lose or broken, or a spring to hold the door open is off or broken.

Nothing blocking, air flow is good, it blows hot air when control is set to cold only on driver side

Nothing blocking, air flow is good, it blows hot air when control is set to cold only on driver side blow hot, duel climate control

The system turns a trap door to divert the cool air into the vents. There may be a control board that is not shutting off the hot water flow into the heater system and turning on the cool air to flow into it. The system blows what temp is allowed to enter the chamber so that switch may be bad. Try replacing the control switch an see if that works.