Amplify slow changing dc signal
Overview
I think our discussion has finally ferreted out the basics. (It took a while and I wish you'd written more at the outset, providing the entire scope and goals, as well as the parts you felt you had working and why you needed what you were asking for to finish it off.) But here's what I gather and think:

You have a slow signal that is basically a \$30\:\text{mV}_\text{pp}\$ AC signal with a \$15\:\text{mV}\$ DC offset relative to ground and operates at about \$200\:\text{mHz}\$.
You already have a nice FET which drives an LED the way you want if it is supplied with a signal varying from \$700\:\text{mV}\$ to \$900\:\text{mV}\$, also relative to ground. For now, I won't ask any further questions about how it's powered or anything else. I'll just assume that this is the working circuit you want driven. (This is where I'm probably most bothered, because of my suspicions that you have merely characterized a single FET and this whole idea won't work well when you get a second one. But I'm just not going to think about that.)
You don't want opamps used.
You are willing to arrange for a DC voltage supply for the pre-amplifier circuit.
At its peak brightness (that you want), the LED uses about \$10\:\text{mA}\$. Because of this fact, I feel that a circuit which uses less than \$5\:\text{mA}\$ is okay. But I'll shoot for a lot less than that, anyway.
I normally would write a lot about how to design things. I prefer something that is more useful over time than just &quot;a gimme.&quot; But in this particular case, you appear to be in a hurry and less interested in the design details than just &quot;a circuit to try&quot; for solving your immediate problem. So I'm just going to write up a suggestion to consider without explaining where it comes from or why.

The idea is the same as I originally wrote in an early comment, where I suggested that you use a long-tailed pair of BJTs, 9 resistors, and a capacitor:



simulate this circuit &ndash; Schematic created using CircuitLab
The capacitor should be at least \$C_1=68\:\mu\text{F}\$, I believe. But you can adjust it up to 10 times that value. The purpose of changing the value of \$C_1\$ is to adjust the overall gain of the circuit to get about what you want with the LED brightness variations.
You can use either node \$A\$ or node \$B\$ to drive your FET. I don't know (or care) which of the two you use. They will be of opposite phase, so one of them will do what you want and the other one will do the opposite of what you want. Both, though, can be used to drive your FET circuit. They are ground-referenced and once you get \$C_1\$ dialed in for the right gain, things should work okay.
Other than that, \$R_9\$ is a &quot;current source&quot; that supplies about \$160\:\mu\text{A}\$ into the BJT pair. This current is driven more to one side, or more to the other side, as your signal changes. This diversion back and forth, together with the values for \$R_1\$, \$R_2\$, \$R_3\$, and \$R_4\$, provide the gain and the offset you wanted.
I chose relatively &quot;stiff&quot; values for \$R_5\$, \$R_6\$, \$R_7\$, and \$R_8\$ so that the base voltages should stay pretty solid. This will require about \$1\:\mu\text{A}_\text{RMS}\$ of compliance current. But since you said the impedance of your source was low, I think it should have no problems here.
If you need to move the output voltage of \$A\$ or \$B\$ up or down a little, then add or subtract a little resistance from \$R_9\$. I worked things out to be closely centered on \$800\:\text{mV}\$, but that doesn't mean it is going to come out perfectly, first time out. So just make minor adjustments (insert a series resistor of small value or do that AND lower the value of \$R_9\$ if needed) to the \$R_9\$ value so that you get the output offset you need. But I think this will be pretty close for you.