They are both grammatically correct, and since they are both in the simple past tense, they both mean the same thing. (That the subject no longer has the room.)
"I had a rented room" implies that you had a room that was rented. The sentence, however, does not imply you directly or indirectly rented it yourself (such as "I had a rented room from a friend". It is a grammatically correct sentence.
"I rented a room" implies you went and rented the room personally, not indirectly. It is also grammatically correct.
They do not mean the same thing, but if I had to choose the latter of "I rented a room" sounds less awkward.
"I had a rented room" implies that you no longer have the room.
"I rented a room" means that at some point in the past you rented a room - you might still be renting it, or you might not be. There is no way to determine that.
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They are both grammatically correct, and since they are both in the simple past tense, they both mean the same thing. (That the subject no longer has the room.)
"I had a rented room." breaks down like this:
I = subject
had = simple past verb
a = article
rented = participle adjective describing "room"
room = noun
"I had a rented room." could mean several thing.
There was a room in my house that was rented to someone else at a point in the past but this is no longer the case.
There was a room in a house/apartment/hotel etc. that I rented for my own use sometime in the past and this is no longer the case.
I rented a room. Means that sometime in the past you rented a room for your own use and this may or may not be the present situation.
With both sentences the context of the paragraph where they occur should make the meaning very clear.
"I had a rented room" implies that you had a room that was rented. The sentence, however, does not imply you directly or indirectly rented it yourself (such as "I had a rented room from a friend". It is a grammatically correct sentence.
"I rented a room" implies you went and rented the room personally, not indirectly. It is also grammatically correct.
They do not mean the same thing, but if I had to choose the latter of "I rented a room" sounds less awkward.
I rented a room
"I had a rented room" implies that you no longer have the room.
"I rented a room" means that at some point in the past you rented a room - you might still be renting it, or you might not be. There is no way to determine that.
"I had a rented room" is past perfect, so it's a completed action. There once was a rented room, but no longer is. Follow?
"I rented a room" is past tense. There once was a rented room and there might still be.
They mean the same but the time frames could be different depending on context. 'Had rented' is further in the past than 'rented'.
They are both correct!