Either past perfect or present perfect is okay, but using the past perfect would be better in my opinion as it doesn't surprise the reader halfway through the sentence. With present perfect, the sentence starts out sounding like you might be writing a positive review, not explaining a problem you have had. (Update: I just saw you changed your question to ask about past simple instead of past perfect. Past simple would also work fine, but I still think past perfect is best for the same reason.)
I had ordered from them many times and never had any problems, but last time I made an order for "Damned" by Supertempo and did not receive the record. I sent many emails but none of them were answered. I finally got a refund after a Paypal dispute.
There are a few other issues I've corrected above. Instead of "got any problem" it should be "had any problems." You could say "hadn't had any problems," but I think it sounds better using "never had" instead. I think supertempo is the name of a band, right? If so, you can't use "the" how you did -- you should use "by" instead and put it after the title. The way you have it now reads like supertempo is a type of record (and maybe it is, I'm not sure). It should also preferably be split into multiple sentences.