Couple things:

Computers NEVER fix themselves.

Windows 7 Gateway should be fine.  You should have gotten a disc with it.  Sometimes, on a Gateway, they have a separate partition on your hard drive to reinstall the operating system and all the programs that came with it.  It MAY wipe out all your documents, pics, files you create since you bought it, so make a back up before you reinstall.

It must have worked when you first got it, right?  Was it faster and did it start up sooner?

There is a thing called "bit rot," that happens to all forms of computer media (as far as I know).  It can cause lots of problems.  It's normal/abnormal.

You may have problems that won't fix themselves, unless you really know what you are doing.

Monitor size has nothing to do with rendering speed, only good for looking at, but yes, bigger is better, usually.  Depends on resolution.  Your new computer probably has external port and you "could" hook up a bigger monitor.

If you have made a back up of your Gateway Windows 7 computer, and you completely wipe the hard drive and reinstall fresh, I would bet your Poser problems would be gone.

If you don't know what you are doing it might be worth it to take it in somewhere where they do that sort of thing.  Geeksquad or similar.