No problem about the questions. Ask away until you get the answers, that's what we're here for :smile:
The calculator results are only a guideline, not completely accurate, which is partly why we recommend going for more power than you actually need. Also, you weren't too sure about entering the details so you may have missed out things like USB devices, fans, capacitor aging, etc.
All PSU's power output decreases over time, so after a year it will be much less efficient than a brand new one.
OK, if you want to keep your 300W PSU then you're taking a risk. The extra load will push up system temperatures, causing artifacts to appear on the screen, games to crash and possibly damaging components like RAM and graphics card. You'll have to go for a low quality graphics card that uses very little power and is not too demanding on the +12V line.
A cheap PCI-e card will improve your gameplay in terms of frames per second and the level of detail you can select in the game's options, but the improvement will be minimal. If you really want better games, you'll need to upgrade the PSU so it can handle a better graphics card.
Cheap GeForce 7200GS $34 - http://www.newegg.com/Product/Product.aspx?Item=N82E16814125071
Could it be something else causing your system to be slow? You mention slow startup times. This can usually be improved by editing the msconfig startup list, removing unnecessary entries. There might be some other Windows tweaks to help speed things up without having to spend anything on new components.
Note: I'll move this thread over to Hardware > Graphics Cards.