So, parallel tasks can't override each other?.
They can; in fact you created a perfect example of that in your original post.
The challenge is in achieving what you want to achieve, avoiding things working in ways other than you desire or intended.
The main problem here is that it's not at all clear what you are trying to achieve, what you want to happen, or what would need to be done to implement that using parallel processing to make it work as desired.
I was hoping to use code0 to flash a light sequence, and code1 to monitor a button press, which then affects code0.
You will have to provide more detail on that, what the light sequence is and how you want it affected, for people to help with that but here is a simple multi-tasking program which affects the speed of the C.1 LED flashing depending on whether the button is pushed or not -
Code:
#Picaxe 08M2
Start0:
Do
Toggle C.1
If b0 = 0 Then
Pause 1000
Else
Pause 240
End If
Loop
Start1:
Do
If pinC.3 = 0 Then
b0 = 0
Else
b0 = 1
End If
Loop
Here's an alternative, possibly more elegant way, of doing that -
Code:
#Picaxe 08M2
Start0:
Do
Toggle C.1
Pause w0
Loop
Start1:
Do
If pinC.3 = 0 Then
w0 = 1000
Else
w0 = 240
End If
Loop
And here's a version which is more responsive whenever the button is pushed or released -
Code:
#Picaxe 08M2
Start0:
Do
Toggle C.1
w1 = 0
Do
Pause 40
w1 = w1 + 40
Loop Until w1 >= w0
Loop
Start1:
Do
If pinC.3 = 0 Then
w0 = 1000
Else
w0 = 240
End If
Loop