They keep the LCD? That's not a question, that's an answer for you. It simple says they are planning on stealing a high dollar part from you. Stay away from these thieves!
Please give us your model number from the bottom of the stand.
The PSU is probably all you need:
27" Apple LED Cinema Display 250W Power Supply
Item #: 661-6048 1011969
Replacement, 27" Apple LED Cinema Display 250W Power Supply
Here's one at Amazon for $105
I wouldn't bother going back to the shop. All they are going to do is deny they were trying to steal your LCD. Even if they were not, the proper order for repairing this is the power supply first.
Before you spend any money thy these possible fixes:
Power Cycle for 30 Seconds
Thunderbolt-Display-RearShut down and disconnect both your Mac and Thunderbolt Display from AC power for at least 30 seconds.
Disconnect the Thunderbolt Display's MagSafe cable from your Mac.
Disconnect the Thunderbolt Display from AC power by unplugging the cord.
Disconnect all USB peripherals and any cables plugged into the Thunderbolt Display.
Wait at least 30 seconds before powering on your Mac and Thunderbolt Display.
Reset Your Mac's SMC
SMCIntel-based Macs have a System Management Controller (SMC) that can be reset as a possible fix for Thunderbolt Display issues.
These instructions are for Mac notebooks with non-removable batteries.
Shut down the Mac.
Plug in a MagSafe or USB-C power adapter to a power source and to your computer.
On the Mac's built-in keyboard, press the left side Shift-Control-Option keys and the power button simultaneously.
Release all the keys and the power button at the same time.
Press the power button to turn on the Mac.
Apple provides steps for Macs with removable batteries, and the Mac Pro, iMac and Mac mini, on its support website.
On Macs with MagSafe power adapters, the cable's LED might change states or temporarily turn off when you reset the SMC.
Reset Your Mac's NVRAM or PRAM
NVRAMNVRAM, short for "non-volatile random-access memory," stores certain settings even when your Intel-based Mac is turned off. On older Macs, it is known as PRAM.
Shut down the Mac.
Turn on the Mac.
Press and hold the Command-Option-P-R keys immediately after you hear the startup sound.
Hold these keys until the Mac restarts and you hear the startup sound for a second time.
Release the keys.
After resetting NVRAM, you may need to reconfigure the Mac's settings for speaker volume, screen resolution, startup disk selection, and time zone information.
Use a Standalone Thunderbolt Cable
Try connecting a standalone Thunderbolt cable between your Mac and Thunderbolt Display. If this resolves the issue, then possibly your Thunderbolt Display's dual MagSafe-Thunderbolt cable is damaged.