Actually, I disagree: this sentence does have a coherent meaning in Latin, if my parsing is correct.
Rather than as a noun, I read comploratus as the past participle of comploro which has attested forms of taking the accusative (see the first example in the linked entry). It is rare and post-Augustinian, but it is not incorrect.
The rest is not hard to put together, if you understand comploratus as a past participle and silens as a present participle both modifying ego. The last trick would be to put a colon after oro and see "regnet exitium" as direct discourse:
Prodigia comploratus, Having bewailed these [bad] portents,
silens, oro: Keeping silence, I pray:
"Regnet exitium." "Let destruction reign."
Edit:
As @TKR pointed out in the comments, comploratus can only be interpreted as active ("having bewailed") rather than passive ("having been bewailed") if it is deponent. I do not see any precedent for this, so it turns out that the phrase is bad Latin, because a passive participle cannot take an accusative direct object in this way.
I still think that this is a more probable interpretation of what they were getting at and shows perhaps a little more effort on their part than visiting our friends at Google Translate.
Edit 2
Per Cerberus's comment, there is another grammatical interpretation, though its meaning is less clear. Since sileo (like taceo) can take an accusative object to mean, "to keep X silent", we could interpret complaratūs (4th declension) as genitive and prodigia as the object of silens. We thus get:
Keeping silence over these portents of grief, I pray: "Let destruction reign."