The TD04 is plain bearing turbo so there should be a little sideways play on the shaft (which is taken up by the high pressure oil feed from the engine so the bearing 'floats' on the oil film) but no give from front to back. The shaft should spin quite freely and smoothly without any roughness or ginding/scratching. If there are marks on the compressor housing where the blades have touched, then the bearings are shot. If the compressor blades are bent or chipped this can throw the wheel out of balance taking into account these things can, in theory, spin up to 100K rpm. Do you have access to a camera so that you can take a photo down the inlet and put it up here for us to see?
As far as worn bearings go, this is not the end of the world as rebuild kits are widely available but it depends on your mechanical skills and how adventurous you are as to whether you tackle a rebuild. The first time I did it (I've now stripped, modified and rebuilt this particular model around 10 times) I was stepping into an unknown realm but I found an excellent pictorial tutorial for a Volvo TD04 rebuild (except for the inlet and outlet castings, it's essentially the same unit) that made the job quite easy. If you decide to do this, let me know and I will see if I can guide you in the right direction and pass on a few vital but rarely published tips I picked up along the way. If you bought a rebuild kit and gave it to a mechanic to do, by the time they have charged for their work, although your turbo is now almost as good as new, you might have spent more than replacing this suspect one.
As you haven't posted your country location this is a tricky one to advise on. There was a chap last year from Israel who came on the forum briefly after buying a bit of a dog (S turbo) and the prices he was showing for buying replacement parts, relative to import taxes etc into Israel, were quite astonishing. If this is your location, rebuilding, whether you do it or get someone else to do the job, might be the more economical approach.
The other thing about this purchase is that the 03 Forester turbo (XT) for the European market came with a TF035 turbo which is somewhat smaller than the one you have bought. Replacing this with a TD04 is easy enough in that it is a direct bolt on fit and uses the same parts the TF035 uses (oil/coolant lines etc) but, upgrading to this blower will require a re-map because the TD04 delivers a bigger charge of air and has a higher boost pressure capability, so unless you drive it like a granny you could damage your engine substantially. The remap is specific to your car so don't be fooled by any of these "chips" you see for sale that make outlandish claims. Chips are things to be eaten with fish in the UK and dipped in sauce everywhere else, not inserted into a turbo charged engines management system. The TF035 to TD04 is however a cost effective upgrade and gives gratifying grins all around for a reasonable expenditure.
What is the situation with mapping services in your locality? If the commonly used "Ecutek" system is not available to you there is another way called "Open Source Tuning" which requires a reasonable degree of understanding, a laptop, the appropriate software and a special connector cable. In very simplified terms, You link the laptop to the data connector (under the steering column) and log the engines behaviour. This is then sent to a tuner, by email, probably in the US, who writes a modified map for your engine and emails it back to you, for a fee of course. You then reconnect the laptop and download the new program. If it works straight off, great but often it will need fine tuning and so you build a relationship with the mapper. More info on this can be found in the "Engine Management, Tuning and Datalogging" section. Finding and using a recommended mapper is essential too.
OST usually works out less expensive than the Ecutek setup because there is no license fee involved but the program writers are mostly benevolent donators who constantly work on and publish the upgrades to the tuning software. Are there any tuners within traveling distance, usually guys who have a dyno? These fellas sometimes use Open Source and you are paying them for their time only. With an Ecutek remap, you pay for the initial license and the mappers time, which can be quite costly depending on your territory, and then the mappers time for any tuning tweaks thereafter but, you have to go to them or in our case (Ireland) we have access to "Jolly Green Monster", aka Simon Roe who comes over here 3 to 4 times a year depending on demand.
Also, I am assuming you are driving an XT, is this the case? The more info you supply, the more folks will chip in and help but if they aren't certain what your location and derivative is then those with the knowledge relative to certain subjects are not inspired to step forward. TD04s? I have learned a bit and always help where I can when someone asks about them :smile:.