MacBook Pro suddenly really slow, hangs often

Question

My MacBook Pro is about 2 years old. It had been slowing down and occasionally running out of memory, which I figured was due to the fact that my hard disk was kind of full (had about 100 Gig of space available, which I thought should be enough, but whatever). But in the past 2 days this has gotten really, really worse. It's almost unusable. It's running Snow Leopard.
It takes a full 5 mibutes to start.
When I open an application it takes really long to open, then evey few things I do it hangs for a couple of minutes with the rainbow wheel spinning. Occasionally an application completely stops responding, and has to be force quit.
This even happens if I have only one app open at a time.
What has changed recenttly:
• 2 weeks ago I switched from DSL to cable. I have a new cable modem and wireless router. There is some random software that Comcast sent me but I don't think it's even installed.Things were still running slow and frustrating but pasable after that.
• 5 days ago I bought a new Droid 3 cell phone, and installed The Missing Sync on my computer to sync music, photos and calendar. It still ran slow after that, but not crazy messed up like now. I don't remember if the speed seemed any worse -- I just know that it didn't hang often the way it does now. 
• 2 days ago I bought a new MacBook Pro with a faster processor, runnign Lion. I started migration assistant, then realized it was going to take 14 hours and I had work to do, so I stopped the assistant. and decided to run it again later. I think it's since then things became a complete mess, and every day that passes seems worse.
• In the meantime, I may or may not have installed some software updates. I get update notices all the time, and generally install them right away without giving them much thought. In fact, now that I think of it, Firefox startded acting pretty slow after the last update (spinning wheel when opening new tabs, loading information, switching from one tab to the other), which I attributed to a buggy new release but it might be related. I don't know how long ago that was; I think about a week or two. There may have beensome OS udates too, I can't remember.
I did run migration assistant again late last night, after cleaning out my old hard disk (backing things up to DVDs and external drives) so it would have less data to transfer. But it transfered over everything, including old apps thatI don't need and don't know how to uninstall, and I am worried that I might have transeferred over whatever the problem was with the old computer. I can't easily test because the apps that I use every day (Microsoft Office 2008 and the Adobe Creative Suite CS4) don't run on Lion so I will have to buy upgrades for everythign before I can do any work on this computer, which is quite frustrating in itself but a different story. So I haven't been able to test whether my new laptop has the same problem; it does generally seem faster but not as much of a speed increase as I had hoped.
I ran disk utility on the old laptop, and it did find some directory issues, but I can't repair it because I don't have any discs to start up from. Why is it that Apple doesn't ship disks with its software? Granted, my new laptop runs a different operating system from the old one, but I didn't receive any system disks with it so I really don't have anything to start externally from if there ever are any problems.
I want to keep the old mac. I occasionally travel to countries where I don't feel comfortable bringing a new expensive computer, so I intend to use my old computer as a travel laptop and the new one as my primary work laptop in my home office. But that means that I don't want to have to throw out the old one, I need to get it working again.
(also, until I install the Microsoft and Adobe upgrades, I can't do any work on my new laptop and I have deadlines to meet that I will need to continue working on with the old laptop) (which, in fact, makes thisissue rather urgent -- I ned to keep working while it's being resolved)

Answer 1

OK, so someine suggested I run AppleJack -- it did make some repairs and now Disk Utility doesn't see anything wrong with my directory, but still finds some permissions problems. Almost all of them seem to be in System/Library/CoreServices/Front Row.app. Says:
should be -rw-r--r--, they are lrw-r--r--
Do I need to fix these or can I leave as is? What is Front Row? Does it make any difference who has permissions on these if they are for a program I don't use?
Also:
stalling problems seem to have been resolved for now (I opened 3 different apps and they seemto work OK). But I still have a problem with the Microsoft Office applications -- I can't easily switch to/from Excel or Word from/to any other apps, I can't CTRL-TAB and select the app, I have to go to that app's window (means moving other windows around until I can see it) and click on it to switch to that app. It's doable but a nuisance. Can it be fixed?
Also - important:
Would the directory problems I had on my old hard disk have affected the information I ported over to the new laptop yesterday? Will I have the same problems on my new laptop? I can't check because I haven't downloaded the upgrades to Microsoft Office and to the Adobe CS Suite, so I pretty much can't open hardly any programs on my new machine right now.  I thought maybe I should run Applejack on that too, just to check, but apparently it doesn't work with OSX 7 Lion.