relay module has 12V power supply, ...
have connected all the Rpi GPIOs relay board, ...
connected 5V and 3.3V connections to the two 5V pins on the relay module (5V is being used to power the touchscreen display) , ...
Run code, nothing happen, ...
It is not clear why you connect 3V3 power to 5V. And it is not clear
if your 12V power relay accepts Rpi GPIO 3V3 signals.
The most newbie proof way is to use 3V3 relays which are a bit
expensive (see Appendix A below).
Cheapy relays are mostly 5V powered, but only those High level trigger
types are almost guaranteed to work for Rpi.
Almost half of those Low level triggered relay work for Arduino, but NOT work for Rpi (See Appendix B for get around).
And avoid using 12V powered relays, because newbies always connect the
wrong wires to Rpi GPIO.
Appendix A - [Expensive/Industrial grade] Rpi Compatible 3V/5V Relays (US$15 ~ US$30)
PiFace Raspberry Pi Relay Board - £27
WaveShare Raspberry Pi Relay Board - $19
SeeedStudio Raspberry Pi Relay Board - $25
I2C Interface DockerPi Four Channel Relay Module - Seeed Studio - US$19
Amazon WaveShare Raspberry Pi Compatible Relay Module with photocoupler - XYG Study US$24
Amazon Electronics-Salon RPi Compatible (Panasonic) Relay Module - Electronics-Salon UUS$17
Using the Seeed Studio Raspberry Pi Relay Board - JM Wargo 2017feb14
Appendix B - Get Around for Arduino Compatible Low Trigger Relay not Working for Rpi
Get Around for Arduino Compatible Low Trigger Relay not Working for Rpi
*Appendix C - Forbes Recommended, with JD-Vcc jumper, Optoisolated, Low Level Trigger 5V Relay (US$7)*
5V Relay for Raspberry Pi Home Automation US$7 - Forbes Finds 2018jul12
Forbes Recommended Amazon Rpi Compatible 5V Relay Module - US$7
Errata - The product spec says each channel needs 15mA ~ 20mA to drive.
THIS IS PLAIN WRONG! I measured a couple of similar relay modules and
found each input end takes only 3mA to 5mA. In other words, the
current sinking requirement is OK for Rpi GPIO pins.
Opto Isolation Consideration
This Forbes relay module has opto isolation, therefore the risk of resultant back EMF, EMI transients flying back to Rpi is much reduced, so your Rpi can live longer! You can even reduce back EMI / EMI by using "total optical isolation" (Must/need JD-Vcc jumper, see references and appendices for more details)
Appendix D - Cheapy Single Channel 5V Relay Modules for Poor Hobbyists (US$1)
For hobbyists and newbies, I would like to recommend the dirt cheap
single channel, no optoisolation, high level trigger modules. Just now
I googled "5v relay module raspberry pi" and found 200+ results.
Google search results for "5v relay module raspberry pi"
I found the Keyes KY019 relay module which I have tested OK for Rpi.
Keyes KY019 Single Channel 5V High Level Trigger Relay US$1 each
Ky019 and other relays: Compare and Contrast - A rpi.org forum discussion
Appendix E -I2C Interface Relay
DockerPi 4 Channel Relay Module - Seeed Studio - US$19
DockerPi - GitHub
52Pi Relay Modules Catalog - 52Pi