I have a huge Tannoy PS350B sub from back in the day. 15" woofer. A while back something started happening with the amp where it just wouldn't power on, randomly. one day it would work, the next day no good. it never blows the fuse and I don't see any swollen caps. The days that it worked became less and less and now never powers up. Anyway, my question is: There is a brand new plate amp from a Def Tech Supercube I for sale, but that apparently is a 1500W amp! I am not worried about the plate not fitting, I will figure something out, but will this be way too much power for the Tannoy 15" woofer which only came with a 350W amp?
It is not the power that is your problem.
That sub of yours is a ported sub with a sixth order alignment, not the usual fourth order alignment. So your sub is a QB 6 box and not the usual QB 4 box.
I don't believe QB6 boxes and alignment have come up before on these forums. However to cut a long story short, a QB 4 alignment will work, and should be used with a straight amp and one pair wire connection. It is an entirely passive arrangement.
A QB6 box on the other hand needs not only acoustic tuning of the box, but also an integrated specific electronic equalization circuit in the amp as part of the system tuning. There is no passive solution.
This alignment had a vogue quite a few years back and KEF had a flagship speaker with this alignment, with a specific equalizer in the tape loop. People never understood it and it was a commercial failure. They had an excellent bass however.
Now your sub has a pro BASH amp specific for that speaker. It can be used from and LFE output, but also has sophisticated bass management for recording studio mixing.
The Def Tech amp is totally unsuitable, as that has EQ for a small sealed sub. That us a QB2 box. The amp is powerful because sealed box subs are very inefficient as they use gobs of power to provide a 12 db per octave boost below the high F3 roll off point. They also have high pass filter to avoid blowing the driver.
So that sub amp is totally unsuitable for your situation and will almost certainly ruin the driver.
Unfortunately you need an exact replacement amp for your unit, or have yours repaired.
You could use a straight amp, but will no longer be a sub. It will be a bass module with a significantly higher F3.
Unfortunately for you sixth order alignments have been seldom used, are tricky and something few speaker engineers have experience with.
If you can't find another amp or repair yours, it is the end of the road for that sub.