Are trying to access your modem or Router ? If your access is wireless then you could have someone else using one of your connections... More than one connection will Slow down your system..
Click4Support and Geek Squad are total ripoff company's that over charge and will take advantage of you ... I will have to look into the one mention above..
Turn down the speed of it,Try this got to Start buton, Control panel,Next View by Large Icons, then click on Mouse, Next click on pointer Options, Then Move the Motion to a slower setting..
There are allot of Free Antiviruses out there, And it just comes down to what you like.. Avast is good, I use 360 internet security.. You will just have to try some for yourself...
What type of Monitor is it ? LCD / LED or older ? I would try a different Monitor to rule out Video... Onboard Video can also go bad.. Is this a desktop or Laptop ?
A Desktop is Way better for you and you will have allot more control over the way it runs, The i7 does run hotter than the i5, but this will come down to your case and how many fans you will need.. Heat can play a big Problem on ANY computer/laptop ..
What OS came in this laptop? Here is a link for Windows 7 32 bit drivers...
http://www.downloadlaptopdrivers.net/2013/08/dell-vostro-1550-drivers-windows-7-32.html