First, IF the second TV is close by you should look at whether you could send it signals as Composite Video and L/R stereo sound on a common 3-line patch cord, instead of RF.
However, assuming the cable run distance is too far for that, you probably do need to send it an RF signal on coax cable. But your post confuses me a little. At first I assumed you want to send to the second TV the RF output from the computer you're building, as a replacement for the RF Out from your existing Topfield. Then you say, "how do I run the TV signal that will be entering the Tuner Card out to the other TV?" This sounds like you will have an RF signal on coax entering the new computer's tuner card (Hauppauge T500) and you simply want to split this input into two cables going to the Hauppauge card and the second TV. This splitting is easy - a 2-way coaxial splitter does the job. If there is any concern for signal strength over long cable runs, a decent wide-band cable TV amplifier will help. You do NOT need one that covers up to 2 GHz for Satellite systems. The UHF and digital channels on any cable system only go up to 700 to 800 MHZ, so an amp and splitter with a bandwidth to 1GHz is sufficient.
However, you appear to have a different problem - you seem concerned that you will not have any RF signal to send to the second TV. You imply that your new computer will have VGA and HDMI outputs, maybe DVI. Each of these has signals very different from either standard-def analog TV or digital TV (standard- or high-def), so converting them to some TV signals and them modulating them onto an RF carrier takes a significant conversion box. I honestly don't know how well those devices work.
Another option is to output from your HTPC the old standard Composite video signal (sometimes available directly, or with an adapter from an S-Video port) plus the 2 stereo audio channels and use a simple RF modulator to convert those signals to RF. Then we have the channel matter to settle.
Many common RF modulator adapters output only a few channels, often in the VHF-Low band (channels 2 through 6). As the conversion to digital TV proceeds, most of those new signals are being broadcast on UHF frequencies, although theoretically digital TV could be done on any existing TV channel. So we come to the question of what channels your TV can handle? If it's a digital TV tuner system, is it restricted to the UHF channels, or does it handle also TV on the two VHF bands? If it does, then your choice of RF modulator adapter is unrestricted by the TV's tuner. Let's not forget that the Composite Video signal I suggested using is not digital, so the RF signal generated is likely the old analog TV RF signal.
If you need the RF to be in the UHF band you would need to do some hunting for a suitable RF modulator. Moreover, if you expect to send a digital TV signal on a UHF channel to the second TV, your choice of modulator gets trickier, and you also have to find a suitable set of digital TV signals from your new computer to the modulator.