Cambridge Audio CD Player Has Died

Yes, there is a discernible difference in the audio quality of CD players but my experience has been that the difference in the quality of the DACs inside the players has considerably more to do with that than the transport.

So, you might approach this in different ways, buy a new player, buy a separate DAC and transport, or buy a DAC first, connect it to your Cambridge's digital output and determine whether the problem with the Cambridge is the analog output or the DAC. If it works with the external DAC you're done. If it doesn't you could buy a transport for your new DAC and also be set up to use the DAC with streaming devices.

There are a lot of very good DACs out there at reasonable prices. I recently got a Pro-Ject Pre Box S2 Digital for $400 that sounds very nice, has an integrated headphone amp and can be used as a preamp. But there are lots of options you could explore.

I agree that putting more money into the Cambridge probably isn't a good idea.

Your player has both optical and digital outputs so you would connect one of those outputs with the appropriate cable to the input of a DAC and it would bypass the internal DAC in the player. But, since the output of the player is intermittent there's a good chance the issue isn't the DAC since it has no moving parts and the transport does. No way to know without testing, either by buying or borrowing a DAC or taking it to a repair shop. If you do want to test it yourself there are decent, relatively inexpensive DACs like the Topping MX3. For testing purposes you could use a single RCA to RCA cable for the coax connection rather than buy a purpose-built digital cable.

Or, you could be satisfied you've had many years of excellent service for your player and find a replacement. That would be my recommendation. Even if your transport isn't the problem now it will be some time in the future. It's a mechanical device that spins at very high rpm and will fail eventually, just like the tires on our car.

You're right, that's the obvious question and there's no right answer.
As with almost every question that's asked on these forums the first words of the answer should always be, "It depends."

Advantages of the one-box solution -- Simplicity, takes up less space and requires at least one fewer cable. In theory, the manufacturer has taken some care to match the two components and the total manufacturing cost is less than for two boxes. Disadvantages -- You already know the major one, if one of the components fails you're out of music. In addition, transports aren't being improved since the need for that technology is disappearing, while DACs are improving at a rapid rate, for now. It's often very difficult to find a replacement transport mechanism for a device only a few years old.

Advantages of the two-box solution -- Flexibility, being able to use the DAC for multiple sources like streaming, TV audio, etc. If one component fails you have to replace only it. Take advantage of increasingly good digital to analog conversion without having to replace your disc spinner, though there are one-box devices that have digital inputs for use with sources other than the transport.
Disadvantages -- Complexity, twice the boxes and cables. Requires a little more knowledge to integrate properly but that's an issue only once.

An important underlying consideration is that disc spinners of all kinds are an old technology as technologies go and some companies, like OPPO, are already discontinuing manufacturing of players that use them. That will only accelerate and if it survives at all it will be as a niche market with the resulting increase in cost. In a few years it will be as hard to find a transport of any kind as it is to find a SCSI drive for a computer now.