c++ Reading text file into array of structs not working

You always need to check that your input is actually correct. Since it may fail prior to reading 10 lines, you should probably also keep a count of how many entries you could successfully read:

int i(0);
for (; i < 10
       && in >> c[i].barcode >> c[i].type >> c[i].releaseDate
             >> c[i].name >> c[i].purchaseprice >> c[i].rentaltime; ++i) {
    // ???
}

You actual problem reading the second line is that your strings are quoted but the approach used for formatted reading of strings doesn't care about quotes. Instead, strings are terminated by a space character: the formatted input for strings will skip leading whitespace and then read as many characters until another whitespace is found. On your second line, it will read "The and then stop. The attempt to read the purchaseprice will fail because Ring isn't a value numeric value.

To deal with that problem you might want to make the name quotedstring and define an input and output operators for it, e.g.:

struct quoted_string { std::string value; };

std::istream& operator>> (std::istream& in, quoted_string& string) {
    std::istream::sentry cerberos(in); // skips leading whitespace, etc.
    if (in && in.peek() == '"') {
        std::getline(in.ignore(), string.value, '"');
    }
    else {
        in.setstate(std::ios_base::failbit);
    }
    return in;
}
std::ostream& operator<< (std::ostream& out, quoted_string const& string) {
    return out << '"' << string.value << '"';
}

(note that the code isn't test but I'm relatively confident that it might work).

Just to briefly explain how the input operator works:

1. The sentry is used to prepare the input operation:
   1. It flushes the tie()d std::ostream (if any; normally there is none except for std::cin).
   2. It skips leading whitespace (if any).
   3. It checks if the stream is still not in failure mode (i.e., neither std::ios_base::failbit nor `std::ios_base::badbit are set).
2. To see if the input starts with a quote, in.peek() is used: this function returns an int indicating either that the operation failed (i.e., it returns std::char_traits<char>::eof()) or the next character in the stream. The code just checks if it returns " as it is a failure if the stream returns an error or any other character is present.
3. If there is a quote, the quote is skipped using file.ignore() which by default just ignores one character (it can ignore more characters and have a character specified when to stop).
4. After skipping the leading quote, std::getline() is used to read from file into string.value until another quote is found. The last parameter is defaulted to '\n' but for reading quoted string using a '"' is the correct value to use. The terminating character is, conveniently, not stored.