Sounds to me like your ECU is dropping into "Limp Home" mode. This is a direct result of the new tyre sensor going active

Turbo motors are low compression; if you disable the turbo, they become notoriously difficult to start, tick over like a cement mixer (if they tick over at all) and lack power. While driving like this, they burn huge amounts of fuel, smell very rich, and if you put your foot on the accelerator, will reward you with a whuff of black soot out the pipe and not much else. I can quote these symptoms verbatim since this is what happened on our Maserati Biturbo.

Given the way your car is behaving, this is also consistent with the ECU going over to LH; in this case, I would guess that the ignition advance has been fixed to a retarded value and the turbo waste gate has been dumped to safe mode (wide open, giving no turbo boost) to stop the engine going into detonation, which would knacker pistons and heads (and other whirly bits too). You do not really want to drive the car much further than you should like this if you can help it as is can cause large amounts of unburnt fuel to go into the sump and this will thin the oil and knacker the crank eventually. Whatever the problem is, I would recommend the first thing you do after the problem is sorted is to change the oil and filter ahead of service interval, and with good quality oil like Mobil 1 which is the dog's doo-dah for turbo engines.

Before you panic, I would think that you have not blown the turbo, since this is a progressive (usually) or instant failure on the road. For the engine to run OK and then get grumpy points elsewhere. Turbo failure is usually accompanied by oil consumption, exhaust smoke (blue, not black) and lessening of performance over time. It can also seize solid, but you would hear that (no turbo whine if the turbine is not rotating). Can you hear turbo whine as you accelerate, before the ECU goes off?

If you are driving for 5 minutes from cold before this starts up, then it sounds to me as if the ECU has just tried to go from cold driving/warmup mode (enriched mixture) having sensed the coolant temperature has reached sufficient level to switch over to the normal mixture mode. As it makes the mode change, it seems as if it is finding that one of the sensors/actuators normally used in normal mode is not operating properly. It then kicks into LH. Since turbo engines need special cold running management strategies, you sometimes find an extra injector to richen the mixture when the engine is cold to stop the charge weakening due to petrol condensing on the cold inlet surfaces. If the ECU went to normal mixture at correct temperature, then it will turn off the enrichment injector. It could be that for some reason the ECU then detects the mixture has gone weak (it looks at the exhaust gas oxygen sensor) and thinks "Ey up! I'm going to go into detonation and seize the turbo! Anchors out!"

I am almost willing to bet you have one dead injector on one cylinder. Pull all the plugs one by one and look at the colour of them all. They will probably look pretty sooty, except one of them. That will be the one with the dead injector. My money goes on this

There are other things that could have failed to make it do this:

- failed MAP sensor, which means the ECU is unable to determine mixture strength by measuring the Mass of Air going into the engine. It then goes to LH and guesses at the volume of air being sucked in by a predetermined value determined by the engineering team during development. Pretty rare, but it happens none the less. Unforch it is also an expensive component, but you should be able to get a replacement from a scrappy for a resonable price.

- collapsed fuel filter; this is cheap and easy to replace, and should be done regularly on injected cars. On a friend's Peugeot, the filter used to collapse and block off the fuel line, starving the engine. This usually only happens if the fuel pump is in suction to the tank, upstream of the filter. If you have an in-tank pump that pressurises downstream of the filter, it is not as likely to happen.

- failed fuel pressure regulator. This one is a classic on injected systems, giving the rough running symptoms you describe. Not cheap to fix, but easy. The regulator usually fails to limit the pressure by either bursting an internal diaphragm (low pressure, lumpy running or bad starting) or seizing (incorrect fuel pressure, affecting mixture strength, causing overheating or "flat spots").

- if you have a single coil directed spark ignition, you could have either a dodgy transformer (insulation brekdown causing low spark voltage, leading to misfiring) or a coil breakdown (gradual loss of power as the coil overheats).

I would suggest that you bite the bullet and get the engine onto a Toyota test system at the garage to eliminate the ECU as a problem. If it is going into LH then there will be a failure code recorded in the ECU to state what it detected to make it go into LH mode. The longer you run it in this mode the more likely you will cause damage to the engine (crank/oil, or pistons/rings) or the Cat (contamination) which will cause you problems with the MOT on emissions later on.

There used to be a very good family-owned garage called Chorley Motors at St. Neots towards Bedford which specialised in injection diagnostics. They had a BOSCH diagnostic system with a rolling road, so if they're still there give them a call, as I found them friendly and very knowledgeable, plus they call a stone a stone, don't baffle you with bull**** and charge a reasonable rate for repairs.