OK. To start with you should know this:
When your computer boots it goes through a few stages. The first stage is the POST. This is where you see the Toshiba logo. This is also where the PC detects and understands the hardware attached to it; such as the CPU, Memory, and boot devices.
Then it will run through the Boot Sequence. Now you can specify the devices you want it to boot from. Usually you want it to boot from your primary hard drive (which is where you would store Windows).
The message you're reading after this; "Exiting PXE ROM" is from the last item on your boot sequence; that's your network. The PC is checking to see if there's a PXE Server out there on your home network from which it can boot. Of course this fails because it's very rarely used if ever by most people.
Now back to the actual issue. There are 2 possible causes for this. Firstly you may have accidentally removed your hard drive from the list of boot devices; therefore it's not even being checked for Windows- hence it cannot find anything to boot from.
As you mentioned previous blue screens however I think the more likely scenario is that the copy of Windows on your hard drive; and the partition is resides in, have become unbootable. This means your computer is still checking the hard drive, but the copy of Windows on it is in such a state that it cannot be booted. Logically it actually means that the MFT or Bootloader on the hard drive is missing or corrupt.
This may be recoverable; HOWEVER as you were previously experiencing blue screens and restarts; I'd strongly suggest you use whatever recovery disc came with your computer to perform a CLEAN DESTRUCTIVE REPAIR / REINSTALL. Doing so will destroy any data on the hard drive, however I honestly think it is the best bet to restore full function to your machine.
If you do this and still experience issues then you may have a faulty hard drive. This is uncommon however does happen; as the hard drive is the most likely part of a pc setup to fail.
If you have data you are adamant about backing up; I'd recommend you download and burn a Linux Live CD; from which you can access your Windows partition (if present) and back up your data to disc, or to USB Storage Device. If you're new to Linux I suggest using a Kubuntu Live CD as it has a UI similar to Windows.
I hope that all makes sense. I know I have a tendency to mention things at times without full explaining them, but as long as you follow the gist you should understand what the possible issues with your PC are.