I tried the 4-digit code in the manual but the arrow keys didn’t work, so I futzed until I found something that worked.
The 4-digit code for the DVD half of the DVD/VCR combo is 1409. I haven’t tried getting the VHS half to work yet, but 1409 worked for the DVD.
I couldn’t find the answer to this elsewhere on the internet, so I wanted to post it here in case it helps anyone else. Please leave a comment if this works for you (or doesn’t).