Kudos for making the test run on a non-workday.
In my opinion, there are three parts to the commute:
1) The attitude - If the attitude's wrong, nothing else can be fixed. Give yourself some time to improve your fitness level (#2) and figure out the "once I get there" steps (#3). If it's too cold or rainy or 95+ degrees, skip the ride. Don't fight those fights when you haven't worked out the basic 70 degrees and clear ride. Most folks would only get discouraged just because they tried a commute that many "experienced" fair-weather commuters avoid anyway. Do whatever it takes to keep your biking/commuting efforts positive.
2) The ride - I ride 9-11 miles one way, so I'm not the best person to empathize with a 4-mile ride. On the other hand, my wife rides about 6 miles each way. She was very out of shape when she started and, although she is still improving her fitness, she can handle the ride comfortably now. She is a slower rider, but she is comfortable. We don't measure our climbing levels, but she has three "hills" that gave her fits for the first few weeks of general riding around town--to the point of stopping and/or getting off to push her bike. Also, she had been riding a lot on the weekends--grocery store, library, coffee shop, restaurants, etc.--before she ever tried a commute. That kept her from dealing with excessive physical strain on the commute and allowed her to work out the details of her routine (#3). Key point for out-of-shape riders--slow down! Unless slowing down would mean stopping, then switch to a higher gear and take it easier. And walking hills is fine too. That worked wonders for my wife. She is proudly aware of the fact that, over time, she has been able to ride in lower gears where she would have had to change gears earlier.
3) The routine - 12 rides. That's the magic number of rides that it often takes new commuters to get the particulars ironed out, especially if there are any unusual issues about their route or work situation. Any frustration before 12 rides is due to low fitness level (see #2) or just not enough iterations to work out the details yet. Be patient! (see #1) Get your things together the night before, at least while you're getting used to bike commuting. That will make the morning's less stressful before you even walk out the door. Also, I kept a diligent ride log that included the temp and what I wore. Within one calendar year, I had a nice list of the right clothing level for 10-degree outdoor temp bands, whether I was commuting to work, riding to downtown, or cruising out to the country. That list went on my phone, and I still check it with the temp/forecast when I'm getting ready. I rarely misjudge the amount of clothing to wear any more. As for the rest of the routine--dealing with hair, sweat, etc.--there are numerous articles on Google about bike commuting that have already been written. I have showers at work. My wife doesn't. We both work in professional office environments, so it can be done in either situation.