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."
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.
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."