There's a bit of confusion in this thread as to what you want to do and what the problem is. If you still want to use your old powermac, it would be worth finding out whether the firewire sockets on the mac is at fault, or whether it's the audio interface, or, indeed, whether it is the cable between them. The cable is the easiest to check (swap it out for a different one and see if that improves things), and the most likely suspect. The audio interface is next most likely, though it's tricky to test without another computer with firewire which can run the drivers. You can test the computer's firewire sockets by plugging in a firewire hard drive, if you have one, and doing a speed test - if the hard drive is stuttery and slow that points to the firewire on the computer, in which case your best bet might be a firewire PCI card; there were several mac compatible cards made in the 90s, which you may find cheaply on ebay. Or, frankly, you might as well buy a new powermac with working firewire - a new g5 can be had for £50, it seems.
If the computer's firewire is fine, then there are many decent firewire audio interfaces available on ebay for very little money. You may well find a replacement tascam.
If you want a modern interface, you will be after a class compliant USB interface (i.e. one that doesn't require a driver). There are many to choose from, and you can get one with average mic inputs for less that £100 (e.g. from Behringer or Presonus). You can pay more, but first you'll be paying for better mic preamps, which aren't necessary if you are no longer recording onto the machine.
But USB won't be much use for you if you want more than stereo, or if you want high sample rates and bit depths, because your G4 only has USB 1.1 ports. Most, if not all, modern USB interfaces are USB 2; USB 1.1 is much slower, so could be tripped up. The USB 2 interfaces *should* work with a USB 1.1 host, though. Note that the G5s had USB 2 on board, so if you had one of those that wouldn't be a problem. Indeed, were I in your position I might well consider buying a second hand G5 and cloning the G4's hard drive onto it so I could reliably use a USB2 interface.
But if you just want to listen to the music already on the machine in stereo, why not use the headphone output? Apple audio hardware isn't bad at all, and a 3.5mm stereo minijack to 2 x 6.4mm mono jack lead can be had quite cheaply. It's sufficiently low tech that you might not have considered it.
And if you no longer want the machine, just the audio files on it, you could, as many have said, transfer files onto a hard drive and listen on your MacBook. Of course, there is no telling how well old daw flies would play back on a modern system, even if you have the same plugins on both.
Hope this has been a useful summary of options. Working with old hardware is full of pitfalls - not least because the manufacturers won't offer support on old systems. Best of luck solving your problem.