Hyundai i30 Diesel automatic won't accelerate above idle at light

Sure, what is your question about the 2011 Hyundai i30 1.6 diesel?

run the fault codes
on the engine there is a fuel control module that could be faulty or bad wiring or connections for that unit
kick down could be a faulty vacuum line or actuation control unit on the transmission

What is wrong with taking it in the shop?

Look at the throttle cable where it connects to the air horn and moves the shaft that controls the butterfly to let air in the manifold .
Even if it says its not adjustable usually is a small stop screw that you will have some control over how far the air inlet butterfly will come to a stop position .This will control the amount of intake air less air slower idle .
However you may have other issues .

usa car, must i have to ask that? huge variances world wide !!!
does it crank, we can watch you or hear what you just did.
see?
which engine? what trans, stick or auto.
the 2011 MK49 jeep.
3.7L gas,
2.0 L World I4 (gasoline)
2.0 L VW I4 (turbo diesel)
2.2 L OM651 I4 (turbo diesel)
2.4 L World I4 (gasoline)

Transmission

5-speed Magna T355 manual
6-speed Aisin BG6 manual
6-speed Hyundai 6F24 automatic
CVT Jatco JF011E automatic
or
Replaced in 2011 by the 2.2 L Mercedes-Benz OM651.
try to know where you live, and what's under the hood
before asking for help. and win.
and does it crank.

generic, cranks
1;check all fuses.
2: get tuneup. filters and per list matching your engine.
3: does test fuel spray work at all.?
4: does cranking wide open throttle clear the flood?(if it is)

Clean the throttle body.

A drivetrain on any powered vehicle is the complete system that makes the vehicle run under its own power. It includes the engine, clutch/torque converter, gearbox, transfer case (for 4wd or awd vehicles) drive shafts, differentials, and axles. You will note that the engine (diesel, gasoline, steam, electric) is only one part of the drivetrain.

Check all vacuum lines. Must be tight fit with no cracks. Cheap to replace.

check bearing

Priced new output speed sensor €190, went to breakers yard, found similar sensor on mitsubsihi carisma, purchased €20, fitted same no problems since. Touch wood!