Read to FAQ (frequently asked questions) about cutting or not cutting the spikes. The choice is up to you.

Sure you might get some flowers from the old existing spike but they will never be things of beauty as per when you first bought the plant.

You do not say where you are in Australia, but here, Sydney, new spikes on many Phalenopsis will be initiated in May/June when inside house temps drop at night.

Thanks Arthur(?),

I had read this FAQ but was confused about whether it applied to me what with the new spikes and bud blast.

I was also not sure whether to cut the spike off at the base, or halfway up and hope for re-flowering, as some sites suggest. I take it you would recommend cutting all 4 completely off?

I'm living in Norway at the moment, where it's winter heading into spring. So the apartment is still heated during the day, down to 10 or 15 degrees at night, and probably will be for a month or two yet.

Thanks for your advice, much appreciated!

You will not get a positive Yes or No cut the spike off at the base because it is a depends situation. If i am on sales table duty at an orchid society show i might tell you to cut the spike down to a node on a standard type Phalaenopsis if i sensed you were not an orchid grower and were just buying a plant as a cheap bunch of flowers.
You should not cut the spike on some of species Phalaenopsis such as Phal.violacea or on primary hybrids with violacea as a parent.
One specialist grower of Phals cuts the spikes off at the base at the end of the show season here (Mid October) but by then his show plants had been out for several months had been to three of four shows and he figures that the plants need a rest and will in any case initiate new flowering spikes the following late autumn.
Passing on giving advice re. growing in Norway. Though at least those night temperatures are sensible.
Going back to the FAQ. Here is a picture of said orchid in the link. It is a tiny little thing that decides to bloom each summer so if you have enough Phalaenopsis you will be able to have some in bloom at most times during the year. In other words not all are stimulated to bloom by the cool down in Autumn.
I have had the plant for at least six years and every year the routine is the same.
Late October, initiate new spike
January Flower
Late March cut Spike down to base
and so on.
Hope this helps and doesn't confuse further. Also seek out complete cultivation notes re. Phals on google. Especially those that relate to growing in climates with very cold winters.

Here is a link that might be useful: Orchid mentioned in FAQ