Anyway to check if 1488/89 are healthy or not?
For a start make sure that the +12V and -12V supplies are valid, they won't work otherwise.
You should measure approx. +12V on pin 14 of both ICs. And about -12V on 1488 pin 1, and on 1489 pin 7.
A simple serial test is to get any terminal emulator (e.g. Term), set serial.device, unit 0, 9600 baud, no flow control and disable local echo. Link pins 2 and 3 on the serial port to loop TX and RX data, then type anything on the keyboard. If TX and RX data are working, you'll see the key presses echoed on the screen which will stop when the loop is removed.
If not, look on 1488 input pin 9 with an oscilloscope, you should see a 5Vp-p waveform with each key press. Bit period = 100µSec. That means the UART in Paula is generating serial data.
Then look at 1488 output pin 8, you should see a 24Vp-p waveform of the opposite polarity as the input.
If that's working, then check the same thing on the RX data path, with the serial port pin 2 & 3 loop in place. i.e. 24Vp-p RS232 signal level on 1489 pin 1, and 5Vp-p TTL signal level on pin 3.
It helps to look at page 4 of the
schematic to understand the circuit. The 1488/1489 are simply a voltage level shifter and inverter. Spares are cheap and readily available from the likes of Element14, Radio Spares, Digi-Key, Mouser, etc.
If there's valid RX serial data on the Paula RXD pin and it's not being decoded, it could be an interrupt problem. But that's another conversation.