The first sentence, "We received your message", can be translated both with the preterite (pretérito indefinido) or the perfect. There is a difference, but it's not nearly as clear-cut as in the English equivalent verb forms. In fact both are used in different dialects.
European (Spain's) Spanish is noticeable for its use of the compound tense (the perfect) in places where the simple preterite would be preferred in other dialects. Spanish newspapers will say e. g.
"Una persona ha muerto y dos han resultado heridas en un accidente..."
"One person has died and two have been injured in an accident..."
where most American Spanish dialects would say
"Una persona murió y dos resultaron heridas en un accidente..."
"One person died and two were injured in an accident..."
Using the compound tense to translate "We received your message" would give it a sense of immediacy, which sounds fine: Hemos recibido suggests we have just received the message and (see?) we're already replying to it! But, again, either tense is fine.
For the second sentence, "I deposited the money as soon as possible on the account", the complement "as soon as possible" should be translated as tan pronto como (me) fue posible or tan pronto como pude (the Spanish translation doesn't work without a verb). Though both Spanish tenses are again OK, the complement sounds wrong with the perfect. It should be all in the preterite:
Deposité el dinero en la cuenta tan pronto como fue posible.
Speakers of European Spanish would maybe employ the perfect in both clauses:
He depositado el dinero en la cuenta tan pronto como ha sido posible.
(I hope someone can confirm that last bit.)