Here are your parts
Parts for Frigidaire FGHS2342LF3 / Refrigerator - AppliancePartsPros.com

Following is the tech sheet.

It could be a compressor problem (re: the start relay is trying to start the compressor and cannot it then overheats and tries again) but there are things I would check before I reached that conclusion.

First find out where the noise is coming from.
Is it from the compressor area?

If yes

Is the condenser/compressor fan on whenever the compressor is on?
If no then check if it gets 120 volts when the compressor is on. If it does and the fan does not turn replace the fan.
Are the front kick plate louvers and rear panel slots clean?If not clean them.
Is the condenser/compressor fan blade clean? If not clean it.
Are the condenser coils under the unit clean? If not clean them.
All the above are to ensure that the compressor is not running too hot.

Check the freezer temperature.
it should be between 0 and 5 degrees F.
If it is too cold set the freezer thermostat to a warmer setting. Then wait 24 hours and recheck the temperature.
This is to ensure that the compressor is not running too much.

When the compressor is on check the voltage across the fan. It should be 120 volts (the same as the voltage in the wall receptacle). The fan and compressor are wired in parallel so they get the same voltage.
This checks that there is not a bad connection etc. that is dropping the voltage to the compressor and therefore it is not starting all the time.

Check the compressor and PTC (start device).
Below is a link on how to do this.
How To Fix a Refrigerator - Appliance Repair Guide - ACME HOW TO.com

Note that if the compressor passes the winding resistance test it tells you that the windings are OK but the compressor may still be no good.

There is no good way to check the start device (PTC) electrically so you have to replace it as a troubleshooting method.

All the above assume that the noise is the compressor trying to start and restart.

If the noise is internal to the compressor it may be that the compressor has a mechanical problem. It may last a long time like this or it may stop working tomorrow. Replacing it would be an expensive repair and it often makes more sense to put the dollars towars a new unit.

I would also chewck the compressor mounts.

Looks like the unit only has a one year warranty but I would double check that.