A model number may help others help you.

First clean the condenser coils under the unit.
Check that the condenser fan is running, if it has one.
Check that the compressor is running should be warm/hot and usually you can feel it vibrating.
Check that the evaporator coil fan is running in the freezer, if it has one.
Check the evaporator coils in the freezer, if the unit has them.

If heavily iced/frosted over you may have a defrost problem.
If patchy or they just have frost where the freon enters them you may be low on freon.

Here is a good link on fridge repair mush of the info also applies to freezers depending on the type.
http://www.applianceaid.com/frig.html

Here is the tech sheet for it
http://manuals.frigidaire.com/prodinfo_pdf/StCloud/216857700.pdf

I would put in an ice cube tray with water or a thermometer and plug it in.
Let it run for at least 8 hours and see what happens.

If it freezes the water or gets down to around 0 degrees F then odds are you had a defrost problem.

Yes, since the door was open the water vapor in the air will condense on the evaporator coils.
Actually it is a very good thing as it indicates the unit/compressor is running OK so it should not be that expensive to repair.

Here are your parts
Replacement parts for FRIGIDAIRE LFFU1765DW3 Frigidaire/freezer | AppliancePartsPros.com

Take a look at Item 23 in Section 3.

First remove the evaporator cover in the freezer so you can see the coils.
Not do not let them de-ice.
If they are heavily iced/frosted over you have a defrost problem.

If yes.
Manually force a defrost cycle by turning the defrost timer cam till the fans and compressor turn off.
Now check the defrost heater to see if it is on.
Be careful you do not want to burn your fingers.
If the heater is on then the timer needs replacing, re: it is probably stalling during it's rotation so is never getting into a defrost cycle.

If not on.
Unplug the unit.
Remove the wire for one side of the heating element from the wiring and measure it for continuity, usually around 20 ohms or so.

If the heater is OK
Remove one wire to the defrost thermostat and measure it, should be 0 ohms when frozen. Note that it opens just above freezing so must be frozen to check it. Also inspect it, if it is bulged at all replace it even if it measures OK.

If both the above are OK then odds are the defrost timer contacts are toast.
Best way to test this is a live test to see if you have 120 volts across the heater/defrost thermostat combo.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.

[COLOR="Blue"]So, this means that it is not closing a contact automatically and starting the defrost cycle? This means I need a new defrost timer?[/COLOR]

Yes
The defrost heater and thermostat check out OK so the timer is the only thing left.