How do I get my TC-42PX14 out off Energy saving mode

Different model, but explained here

https://www.manualslib.com/manual/1179614/Gaggia-Naviglio-Hd8749.html?page=46

In yours it is mentioned here in the manual under 'Standby'.

https://www.manualslib.com/manual/55844/Gaggia-Titanium-Espresso-Machine.html?page=16&term=standby&selected=1#manual

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These blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices.
http://electro-medical.blogspot.com/
Blinking codes details of many popular brand TVs are given. Surf the site with patience.

you may find you have the screen resolution set to high, try changing to 1024x768 and try again. if this works it means your monitor ain't up to the job of your better machines.

This link might help diagnose

You may want to shop for that board or at least consider removal of the HDMI socket in question---tested for shorts there I presume?

If this is a CRT TV, the problem is in and around LOT area or on the RGB driver in CRT PCB.

the most common fault is the maine power suply board check all the capassors forflat tops if any are bulged on top they need to be changed

7 flashes to standby light indicates that there is no IIC bus acknowledge at power-on. To locate the exact fault, and faulty board, is a skilled work. Just visit this site 'Electro-help', and see whether it can help you. Check this link, and select the site.

One fo the simple answers is if you have any of the new energy saving lamps (PL Lamps) is if you have one within 10 feet of the tv, the light inhibits the ir siganl.

Turn off your lights and see.
Hope it helps

Dynamic mode will give you a brighter picture. The energy saving mode runs the lamp at a more efficient level that saves energy at the cost of a slightly darker picture. Based upon your description, I'd guess that the lamp is nearing the end of its useful life. Plan on changing the lamp soon. When you do so, place the set back to standard mode and energy saving.
Dan