Well, I've played a couple of games and if you have time to offer any critique/guidance please feel free:
Game 1, Which started well, but fell apart mid game:
[Black "Computer - Basic"]
1. e3 d5 2. Bd3 Kd7 3. Nf3 Kd6 4. b3 c5 5. Ba3 e5 6. Nc3 Nc6 7. Nb5+ Ke6 8. Nh4 Nh6 9. Qf3 e4 10. Bxe4 dxe4 11. Qxe4+ Ne5 12. Bb2 Ng4 13. Nf5 g6 14. Ng3 a6 15. Na3 f5 16. Qf4 Bg7 17. h3 Nxf2 18. Kxf2 Qxd2+ 19. Kg1 Nf3+ 20. Qxf3 Bxb2 21. Rb1 Bxa3 22. Ne4 Qxc2 23. Rf1 Qxa2 24. Qf2 Qxb3 25. Qe1 fxe4 26. Qb1 Qxe3+ 27. Rf2 c4 28. h4 Bc5 29. g4 Qxf2#
Game 2: Which didn't go well at all really, and I retired:
[Black "Computer - Basic"]
1. h4 e5 2. Rh3 Nc6 3. Nc3 d5 4. d3 d4 5. Nb5 Be6 6. Rg3 Nf6 7. e3 Kd7 8. Be2 Bb4+ 9. c3 dxc3 10. bxc3 Nd5 11. cxb4 Qxh4 12. e4 Qxg3 13. fxg3 Ndxb4 14. a3 a6 15. axb4 axb5 16. Rb1 Ra2 17. Bf3 Kd6 18. d4 exd4 19. Nh3 Ke7 20. Nf4 Rha8 21. Kf1 Bc4+ 22. Ke1 Kd6 23. Bb2 Rxb2 24. Rxb2 Ra3 25. Qc1 Rc3 26. Rc2 Rxc2 27. Qxc2 h6 28. Nh5 Nxb4 29. Qd2 Nd3+ 30. Ke2 g5 31. Ng7 Nc5+ 32. Ke1 Ke5 33. Ne8 c6 34. Qc1 Nd3+ 35. Kd2 Nxc1 36. Kxc1 c5 37. Nc7 b4 38. Nb5 Bxb5 39. Kd1 Bc6
"Only two things are infinite; the universe and human stupidity....
....and I'm not certain about the universe." Albert Einstein
I just comment on the first game for now, not with a full analysis but some observations on certain moves and some hints to think about.
Your first move e3 is unusual, playable but not for a novice perhaps. I good plan is to stake out a stake in the centre with initial moves of your e or d pawns two squares forward. Notice this is how your opponent set himself up.
Your move 2 blocks the advance of your other centre pawn and clogs up your natural development lines. Try to have your bishops behind or to the flanks (or both) of your central pawns.
Also a usual rule of thumb for novices is to develop your knights before your bishops unless strong reasons why not and develop everything so that it can affect the centre four squares or their adjacients. Central control then advance is a good easy to implement plan - it is indeed what your opponent did to you!
Your Move 5 set up some tactics as if he moved his c pawn he would expose his queen but you never tried to exploit it. Advancing your d pawn could have done so if it was not blocked from doing some by your pesky bishop move earlier!
Your move 7 moves a piece twice before you have developed the rest of your army - dont rush things. Get your troops out onto good squares then attack.
Move 8 repeats that same error. Knights on the edge of the board control fewer squares. Count them! "Knights of the rim are dim" (always there are exceptions in chess)
9 Qf3 walks into a fork which he sees in advancing his e pawn. Having your pieces in front of your pawns in the opening makes this tactic open to him. Don't do it!
Hope this is useful for some tips for the future. Will try and look at the other game later. It looks like you were beaten by tactics but actually you were beaten positionally already, the tactics followed as a matter of course...
This is trying to be helpful:
It appears you do not understand the value of the chess pieces? Classically speaking:
Pawn = 1
Knight/Bishop = 3
Rook = 5
Queen = 9
King = Infinity
So, start right there. Try to keep a balance of material (i.e.; both you and your opponent have the same values of pieces in total).
My second comment is you really need to get a grasp of really BASIC OPENING PRINCIPLES and improve your play above the level of a rank beginner. In game 2, h4/Rh3 is a bad plan. One does not have to study hard or long to get a feel for what you should be doing in the opening. Any basic chess book will give you advice on the basic opening principles, but a book is unecessary right now. Start Here: Basic Chess Opening Principles. The internet is a wonderful thing for chess players. Take advantage of it.
Learn them and follow them.
My final comment is to up the level of the computer. It's making really bad moves early (Kd7), and missing basic tactics (BxRh3). You don't want to "think" (your) bad play like that will go unpunished. you don't get better by playing bad competition. You get better by being punished for poor play against good competition and learning from it. Take it off basic mode and enable the opening book if possible - yes, you'll lose alot, but so what. I think you're going to develop bad habits playing it at the level it is now. I'd say if you can put a number on the strength it plays at, set it at the lowest strength above 1200 rating. It should play basic sound chess for your purposes. If it's still making silly moves, simply up the level. Find the sweet spot.
Oh, did I mention Tactics?
Do tactics puzzles until you can't see. Seriously.
There are lots of issues with your game, but you need to be able to identify them and address them individually.
Keep playing - you'll improve.
A good computer opponent
I find this computer to be reasonably good:
You can change the strength and play black if you create a free account.
The tactics training on the site is also great (and free).
Good luck, and have fun.