Seems like an easy shut and close case of a broken cable. The only time the device works is when it is physically held in place. I got the stick around Christmas for my girlfriend so it took about two months to break. Roku on Twitter suggested that I buy a new cable (for a 2 month old device?) and when I asked if it was covered under warranty said that I should try my phone cable.
The power supply for a Roku Express 4k+ is a two (2) piece assemply. It is a USB cable with a micro-usb connector on the device end. The larger USB connector end (USB-A) connects into a power adapter (5volt, 1amp).
The advice to use a "phone cable" is because the power supply is the same as some cell phone charger cables. Many Androids still use/used the micro-USB connector.
----
Although your Roku should be under warranty (1 year return policy), I think you will find it easier and cheaper to just replace the power cable yourself than returning the device to Roku and waiting for a return if deemed to qualify. I usually just buy longer power cables anyways. I had one break off inside the device when my dog stepped on the shorter cable and pulled it off the TV. I have now replaced the shorter ones with longer ones for the devices that require them. (I usually get them for about $5 at Walgreens or King Soopers (grocery store).
You can also buy a replacement cable from Roku https://www.roku.com/products/accessories/roku-micro-usb-power-adaptor, but you can find longer replacements at Walmart, Target, Best Buy, Walgreens, etc.
If you want to try for a Warranty Replacement, https://support.roku.com/article/208757058.