First, I would recomend that you only use the VISA functions. The old serial driver is obsolete and no longer supported by NI. The error 37 means Device Not Found I think. One of the goofy things about the old serial driver was that for com1, you to specify port 0, com2 was port 1, etc. If you only have one com port and you use port 1, that could cause the error. Since you can talk to the instrument in MAX, then stick with the VISA functions. When you try the example and you say nothing happens, do you get an error generated or does the instrument just not respond? Are you sending a command or a query?
The first thing you do with the example is click on the little arrow on the right side of the VISA Resource Name. A list of all available resources should show up. Select the com port that your instrument is connected to. Second, right click on the String to Write control and select '\' Codes Display. As I mentioned, the example does not transmit a termination character. I looked at the driver for the Fluke 2620 and it is sending a CR/LF. In the String To Write control enter *IDN?\r\n. Run the VI with both Write and Read set to On and a small value for the Bytes to Read. If you get soemthing at all in the Read String indicator, then you're close. If you don't get anything, you should get something in the error indicator.